{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T09:57:07Z","timestamp":1774605427013,"version":"3.50.1"},"reference-count":81,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T00:00:00Z","timestamp":1757376000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T00:00:00Z","timestamp":1757376000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2026,3]]},"DOI":"10.1007\/s00034-025-03309-0","type":"journal-article","created":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T10:36:13Z","timestamp":1757414173000},"page":"1745-1771","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A New Approach for Order Reduction in Linear Time-Invariant Systems Using Water Strider Optimizer"],"prefix":"10.1007","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5447-1188","authenticated-orcid":false,"given":"Praveen","family":"Kumar","sequence":"first","affiliation":[]},{"given":"Pankaj","family":"Rai","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3503-6332","authenticated-orcid":false,"given":"Amit Kumar","family":"Choudhary","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,9,9]]},"reference":[{"issue":"6","key":"3309_CR1","doi-asserted-by":"publisher","first-page":"4570","DOI":"10.1016\/j.apm.2012.09.006","volume":"37","author":"DI Abu-AI-Nadi","year":"2013","unstructured":"D.I. Abu-AI-Nadi, O.M.K. Alsmadi, Z.S. Abo-Hammour, M.F. Hawa, J.S. Rahhal, Invasive weed optimization for model order reduction of linear MIMO systems. Appl. Math. Model. 37(6), 4570\u20134577 (2013). https:\/\/doi.org\/10.1016\/j.apm.2012.09.006","journal-title":"Appl. Math. Model."},{"issue":"2","key":"3309_CR2","doi-asserted-by":"publisher","first-page":"1617","DOI":"10.1109\/TIE.2016.2618783","volume":"64","author":"ABH Adamou-Mitiche","year":"2017","unstructured":"A.B.H. Adamou-Mitiche, L. Mitiche, Multivariable systems model reduction based on the dominant modes and genetic algorithm. IEEE Trans. Ind. Electron. 64(2), 1617\u20131619 (2017). https:\/\/doi.org\/10.1109\/TIE.2016.2618783","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"10","key":"3309_CR3","doi-asserted-by":"publisher","first-page":"2875","DOI":"10.1177\/0142331218814288","volume":"41","author":"O Alsmadi","year":"2019","unstructured":"O. Alsmadi, A. Al-Smadi, E. Gharaibeh, Firefly artificial intelligence technique for model order reduction with substructure preservation. Trans. Inst. Meas. Control. 41(10), 2875\u20132885 (2019)","journal-title":"Trans. Inst. Meas. Control."},{"issue":"no. 2","key":"3309_CR4","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1080\/13873954.2010.540806","volume":"17","author":"OMK Alsmadi","year":"2011","unstructured":"O.M.K. Alsmadi, Z.S. Abo-Hammour, A.M. Al-Smadi, D.I. Abu-Al-Nadi, Genetic algorithm approach with frequency selectivity for model order reduction of MIMO systems. Math. Comput. Model. Dyn. Syst. 17(2), 163\u2013181 (2011). https:\/\/doi.org\/10.1080\/13873954.2010.540806","journal-title":"Math. Comput. Model. Dyn. Syst."},{"key":"3309_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2022.117363","author":"Q Aumann","year":"2023","unstructured":"Q. Aumann, S.W.R. Werner, Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods. J. Sound Vib. (2023). https:\/\/doi.org\/10.1016\/j.jsv.2022.117363","journal-title":"J. Sound Vib."},{"key":"3309_CR6","doi-asserted-by":"publisher","first-page":"1548","DOI":"10.1109\/LCSYS.2023.3274698","volume":"7","author":"AK Ayd\u0131n","year":"2023","unstructured":"A.K. Ayd\u0131n, A.O. Ozer, J. Walterman, A novel finite difference-based model reduction and a sensor design for a multilayer smart beam with arbitrary number of layers. IEEE Control Syst. Lett. 7, 1548\u20131553 (2023). https:\/\/doi.org\/10.1109\/LCSYS.2023.3274698","journal-title":"IEEE Control Syst. Lett."},{"key":"3309_CR7","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/s00542-018-3939-6","volume":"25","author":"R Bhatt","year":"2019","unstructured":"R. Bhatt, G. Parmar, R. Gupta, Application of stochastic fractal search in approximation and control of LTI systems. Microsyst. Technol. 25, 105\u2013114 (2019). https:\/\/doi.org\/10.1007\/s00542-018-3939-6","journal-title":"Microsyst. Technol."},{"key":"3309_CR8","doi-asserted-by":"publisher","unstructured":"M. Bonotto, P. Bettini, A. Cenedese, Model order reduction of large-scale state-space models in fusion machines via Krylov methods, in 2016 IEEE Conference on Electromag. Field Computation (CEFC) (Miami, FL, USA, 2016), pp. 1\u20131, https:\/\/doi.org\/10.1109\/CEFC.2016.7816280","DOI":"10.1109\/CEFC.2016.7816280"},{"issue":"15\u201316","key":"3309_CR9","doi-asserted-by":"publisher","first-page":"7225","DOI":"10.1016\/j.apm.2016.03.006","volume":"40","author":"S Bradar","year":"2016","unstructured":"S. Bradar, Y.V. Hote, S. Saxena, Reduced-order modeling of linear time invariant systems using big bang big crunch optimization and time moment matching method. Appl. Math. Model. 40(15\u201316), 7225\u20137244 (2016)","journal-title":"Appl. Math. Model."},{"issue":"10","key":"3309_CR10","doi-asserted-by":"publisher","first-page":"4393","DOI":"10.1109\/TAC.2019.2954354","volume":"65","author":"X Cheng","year":"2020","unstructured":"X. Cheng, J.M.A. Scherpen, Clustering-based model reduction of Laplacian dynamics with weakly connected topology. IEEE Trans. Automat. Control 65(10), 4393\u20134399 (2020). https:\/\/doi.org\/10.1109\/TAC.2019.2954354","journal-title":"IEEE Trans. Automat. Control"},{"issue":"4","key":"3309_CR11","doi-asserted-by":"publisher","first-page":"3221","DOI":"10.1109\/TPWRS.2020.3010891","volume":"37","author":"Q Cossart","year":"2022","unstructured":"Q. Cossart, F. Colas, X. Kestelyn, A novel event and non-projection-based approximation technique by state residualization for the model order reduction of power systems with a high renewable energies penetration. IEEE Trans. Power Syst. 37(4), 3221\u20133229 (2022). https:\/\/doi.org\/10.1109\/TPWRS.2020.3010891","journal-title":"IEEE Trans. Power Syst."},{"key":"3309_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/s00542-024-05767-z","author":"P Dash","year":"2024","unstructured":"P. Dash, M.L. Meena, G. Parmar, A. Sikander, A new mixed order reduction method using bonobo optimizer and stability equation. Microsyst. Technol. (2024). https:\/\/doi.org\/10.1007\/s00542-024-05767-z","journal-title":"Microsyst. Technol."},{"key":"3309_CR13","doi-asserted-by":"publisher","first-page":"8016","DOI":"10.1016\/j.apm.2013.02.052","volume":"37","author":"SR Desai","year":"2013","unstructured":"S.R. Desai, R. Prasad, A novel order diminution of LTI systems using big bang big crunch optimization and routh approximation. Appl. Math. Model. 37, 8016\u20138028 (2013)","journal-title":"Appl. Math. Model."},{"key":"3309_CR14","doi-asserted-by":"publisher","first-page":"5893","DOI":"10.1007\/s00034-023-02393-4","volume":"42","author":"BB Duddeti","year":"2023","unstructured":"B.B. Duddeti, Approximation of fractional-order systems using balanced truncation with assured steady-state gain. Circuits Syst. Signal Process. 42, 5893\u20135923 (2023). https:\/\/doi.org\/10.1007\/s00034-023-02393-4","journal-title":"Circuits Syst. Signal Process."},{"key":"3309_CR15","doi-asserted-by":"publisher","first-page":"4506","DOI":"10.1007\/s00034-023-02304-7","volume":"42","author":"BB Duddeti","year":"2023","unstructured":"B.B. Duddeti, A.K. Naskar, K.R. Subhashini, Order reduction of LTI systems using balanced truncation and particle swarm optimization algorithm. Circuits Syst. Signal Process. 42, 4506\u20134552 (2023). https:\/\/doi.org\/10.1007\/s00034-023-02304-7","journal-title":"Circuits Syst. Signal Process."},{"issue":"4","key":"3309_CR16","doi-asserted-by":"publisher","first-page":"2812","DOI":"10.1109\/TSG.2022.3220723","volume":"14","author":"S Eberlein","year":"2023","unstructured":"S. Eberlein, K. Rudion, Impact of inner control loops on small-signal stability and model-order reduction of grid-forming converters. IEEE Trans. Smart Grid 14(4), 2812\u20132824 (2023). https:\/\/doi.org\/10.1109\/TSG.2022.3220723","journal-title":"IEEE Trans. Smart Grid"},{"issue":"6","key":"3309_CR17","doi-asserted-by":"publisher","first-page":"1113","DOI":"10.1080\/00207178108922585","volume":"34","author":"E Eitelberg","year":"1981","unstructured":"E. Eitelberg, Model reduction by minimizing the weighted equation error. Int. J. Control. 34(6), 1113\u20131123 (1981). https:\/\/doi.org\/10.1080\/00207178108922585","journal-title":"Int. J. Control."},{"issue":"no. 4","key":"3309_CR18","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1109\/TAC.1978.1101830","volume":"23","author":"R El-Attar","year":"1978","unstructured":"R. El-Attar, M. Vidyasagar, Order reduction by \u21131- and \u2113\u221e-norm minimization. IEEE Trans. Automat. Control 23(4), 731\u2013734 (1978). https:\/\/doi.org\/10.1109\/TAC.1978.1101830","journal-title":"IEEE Trans. Automat. Control"},{"issue":"2","key":"3309_CR19","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.advengsoft.2005.04.005","volume":"37","author":"OK Erol","year":"2006","unstructured":"O.K. Erol, I. Eksin, A new optimization method: big bang-big crunch. Adv. Eng. Softw. 37(2), 106\u2013111 (2006). https:\/\/doi.org\/10.1016\/j.advengsoft.2005.04.005","journal-title":"Adv. Eng. Softw."},{"issue":"11","key":"3309_CR20","doi-asserted-by":"publisher","first-page":"1859","DOI":"10.1016\/S0005-1098(01)00139-X","volume":"37","author":"Z Gajic","year":"2001","unstructured":"Z. Gajic, M. Lelic, Improvement of system order reduction via balancing using the method of singular perturbations. Automatica 37(11), 1859\u20131865 (2001). https:\/\/doi.org\/10.1016\/S0005-1098(01)00139-X","journal-title":"Automatica"},{"key":"3309_CR21","volume-title":"Genetic Algorithms in Search, Optimization and Machine Learning","author":"DE Goldberg","year":"1989","unstructured":"D.E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, 1st edn. (Addison Wesley Longman Publishing CO. Inc, Boston, 1989)","edition":"1"},{"key":"3309_CR22","doi-asserted-by":"publisher","first-page":"103214","DOI":"10.1109\/access.2023.3317230","volume":"11","author":"JJ Gude","year":"2023","unstructured":"J.J. Gude, A. Di Teodoro, O. Camacho, P.G. Bringas, A new fractional reduced-order model-inspired system identification method for dynamical systems. IEEE Access 11, 103214\u2013103231 (2023). https:\/\/doi.org\/10.1109\/access.2023.3317230","journal-title":"IEEE Access"},{"key":"3309_CR23","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/s12046-018-0810-5","volume":"43","author":"AK Gupta","year":"2018","unstructured":"A.K. Gupta, D. Kumar, P. Samuel, A meta-heuristic cuckoo search and eigen permutation approach for model order reduction. S\u0101dhan\u0101 43, 65 (2018). https:\/\/doi.org\/10.1007\/s12046-018-0810-5","journal-title":"S\u0101dhan\u0101"},{"issue":"3","key":"3309_CR24","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1109\/TAC.1975.1100953","volume":"20","author":"M Hutton","year":"1975","unstructured":"M. Hutton, B. Friedland, Routh approximations for reducing order of linear, time-invariant systems. IEEE Trans. Automat. Control 20(3), 329\u2013337 (1975). https:\/\/doi.org\/10.1109\/TAC.1975.1100953","journal-title":"IEEE Trans. Automat. Control"},{"issue":"6","key":"3309_CR25","doi-asserted-by":"publisher","first-page":"2105","DOI":"10.1007\/s12555-019-0190-6","volume":"19","author":"S Jain","year":"2021","unstructured":"S. Jain, Y.V. Hote, Order diminution of LTI systems using modified big bang big crunch algorithm and Pade approximation with fractional order controller design. Int. J. Control. Autom. Syst. 19(6), 2105\u20132121 (2021)","journal-title":"Int. J. Control. Autom. Syst."},{"key":"3309_CR26","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/j.cma.2018.03.039","volume":"338","author":"X Jia-Peng Liu","year":"2018","unstructured":"X. Jia-Peng Liu, X.B. Shu, H. Kanazawa, K. Imaoka, A. Mikkola, G.X. Ren, A model order reduction method for the simulation of gear contacts based on Arbitrary Lagrangian Eulerian formulation. Comput. Methods Appl. Mech. Eng. 338, 68\u201396 (2018). https:\/\/doi.org\/10.1016\/j.cma.2018.03.039","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"3309_CR27","doi-asserted-by":"publisher","first-page":"520","DOI":"10.1016\/j.istruc.2020.03.033","volume":"25","author":"A Kaveh","year":"2020","unstructured":"A. Kaveh, A.D. Eslamlou, Water strider algorithm: a new metaheuristic and applications. Structures 25, 520\u2013541 (2020)","journal-title":"Structures"},{"issue":"5\u20136","key":"3309_CR28","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1016\/j.compstruc.2009.01.003","volume":"87","author":"A Kaveh","year":"2009","unstructured":"A. Kaveh, S. Talatahari, Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures. Comput. Struct. 87(5\u20136), 267\u2013283 (2009). https:\/\/doi.org\/10.1016\/j.compstruc.2009.01.003","journal-title":"Comput. Struct."},{"issue":"2","key":"3309_CR29","first-page":"1","volume":"255","author":"M Kchaou","year":"2024","unstructured":"M. Kchaou, M.H.M. Tajudeen, M.S. Ali, R. Perumal, B. Priya, G.K. Thakur, Annular finite-time stability for IT2 fuzzy networked switched system via non-fragile AETS under multiple attacks: application to tank reactor chemical process model. Expert Syst. Appl. 255(2), 1\u201318 (2024)","journal-title":"Expert Syst. Appl."},{"issue":"2","key":"3309_CR30","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/0005-1098(76)90076-5","volume":"12","author":"PV Kokotovic","year":"1976","unstructured":"P.V. Kokotovic, R.E. O\u2019Malley, P. Sannuti, Singular perturbations and order reduction in control theory: an overview. Automatica 12(2), 123\u2013132 (1976)","journal-title":"Automatica"},{"key":"3309_CR31","doi-asserted-by":"publisher","unstructured":"A. Kumar, P. Kumar, P. Rai, A.K. Choudhary, Model order reduction using cuckoo search optimization technique, in 2023 International Conference on Ambient Intelligence, Knowledge Informatics and Industrial Electronics (AIKIIE) (Ballari, India, 2023) pp. 1\u20136, https:\/\/doi.org\/10.1109\/AIKIIE60097.2023.10390282.","DOI":"10.1109\/AIKIIE60097.2023.10390282"},{"key":"3309_CR32","doi-asserted-by":"crossref","unstructured":"A. Kumar, A.K. Choudhary, P. Kumar. Comparison of order reduction techniques for automatic voltage regulator, in 2023 4th International Conference on Communication, Computing and Industry 6.0 (C216) (Bangalore, India, 2023), pp. 1\u20134","DOI":"10.1109\/C2I659362.2023.10430914"},{"issue":"no. 1","key":"3309_CR33","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1504\/IJAAC.2012.045438","volume":"6","author":"D Kumar","year":"2012","unstructured":"D. Kumar, J.P. Tiwari, S.K. Nagar, Reducing order of large-scale systems by extended balanced singular perturbation approximation. Int. J. Autom. Control. 6(1), 21\u201338 (2012)","journal-title":"Int. J. Autom. Control."},{"key":"3309_CR34","doi-asserted-by":"publisher","DOI":"10.1007\/s00034-024-02799-8","author":"P Kumar","year":"2024","unstructured":"P. Kumar, P. Rai, A.K. Choudhary, Order reduction of z-domain interval systems by advanced Routh approximation method. Circuits Syst. Signal Process. (2024). https:\/\/doi.org\/10.1007\/s00034-024-02799-8","journal-title":"Circuits Syst. Signal Process."},{"key":"3309_CR35","doi-asserted-by":"publisher","DOI":"10.1080\/03772063.2025.2469641","author":"P Kumar","year":"2025","unstructured":"P. Kumar, P. Rai, A.K. Choudhary, A novel metaheuristic algorithm of order reduction: diminution and performance analysis of linear time-invariant systems. IETE J. Res. (2025). https:\/\/doi.org\/10.1080\/03772063.2025.2469641","journal-title":"IETE J. Res."},{"key":"3309_CR36","doi-asserted-by":"publisher","unstructured":"P. Kumar, V.K. Ravi, P. Rai, A.K. Choudhary. Particle swarm optimization based approximation and analysis of boiler system, in: 2024 International BIT Conference (BITCON), Dhanbad, India, 2024, pp 1\u20134, https:\/\/doi.org\/10.1109\/BITCON63716.2024.10985590","DOI":"10.1109\/BITCON63716.2024.10985590"},{"key":"3309_CR37","doi-asserted-by":"publisher","first-page":"1177","DOI":"10.1007\/s00542-023-05605-8","volume":"30","author":"R Kumar","year":"2024","unstructured":"R. Kumar, A. Sikander, A. Review and analysis of model order reduction techniques for high-dimensional complex systems. Microsyst. Technol. 30, 1177\u20131190 (2024). https:\/\/doi.org\/10.1007\/s00542-023-05605-8","journal-title":"Microsyst. Technol."},{"key":"3309_CR38","doi-asserted-by":"publisher","first-page":"1670","DOI":"10.1109\/LCSYS.2023.3276299","volume":"7","author":"S Lagauw","year":"2023","unstructured":"S. Lagauw, O.M. Agudelo, B. De Moor, Globally optimal SISO H2-norm model reduction using Walsh\u2019s theorem. IEEE Control Syst. Lett. 7, 1670\u20131675 (2023). https:\/\/doi.org\/10.1109\/LCSYS.2023.3276299","journal-title":"IEEE Control Syst. Lett."},{"key":"3309_CR39","first-page":"137","volume":"35","author":"K Laknejadi","year":"2011","unstructured":"K. Laknejadi, A. Kaveh, A hybrid multi-objective optimization and decision-making procedure for optimal design of truss structures. Transactions of Civil Engineering 35, 137\u2013154 (2011)","journal-title":"Transactions of Civil Engineering"},{"key":"3309_CR40","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1016\/j.compstruc.2004.01.002","volume":"82","author":"KS Lee","year":"2004","unstructured":"K.S. Lee, Z.W. Geem, A new structural optimization method based on the harmony search algorithm. Comput. Struct. 82, 781\u2013798 (2004)","journal-title":"Comput. Struct."},{"issue":"11","key":"3309_CR41","doi-asserted-by":"publisher","first-page":"5980","DOI":"10.1109\/TAC.2022.3179539","volume":"67","author":"J Lorenzetti","year":"2022","unstructured":"J. Lorenzetti, A. McClellan, C. Farhat, M. Pavone, Linear reduced-order model predictive control. IEEE Trans. Automat. Control. 67(11), 5980\u20135995 (2022)","journal-title":"IEEE Trans. Automat. Control."},{"key":"3309_CR42","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.ijnonlinmec.2019.01.016","volume":"111","author":"M Mitra","year":"2019","unstructured":"M. Mitra, S. Zucca, B.I. Epureanu, Dynamic model order reduction of blisks with nonlinear damping coatings using amplitude dependent mistuning. Int. J. Non-Linear Mech. 111, 49\u201359 (2019). https:\/\/doi.org\/10.1016\/j.ijnonlinmec.2019.01.016","journal-title":"Int. J. Non-Linear Mech."},{"issue":"1","key":"3309_CR43","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1109\/TIA.2023.3328805","volume":"60","author":"A Miyamoto","year":"2024","unstructured":"A. Miyamoto, H. Sauerland, H. Xu, R.W. De Doncker, Automatic model order reduction technique for real-time temperature monitoring of oil-cooled electric machines. IEEE Trans. Ind. Appl. 60(1), 477\u2013485 (2024). https:\/\/doi.org\/10.1109\/TIA.2023.3328805","journal-title":"IEEE Trans. Ind. Appl."},{"issue":"1","key":"3309_CR44","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1109\/TAC.1981.1102568","volume":"26","author":"BC Moore","year":"1981","unstructured":"B.C. Moore, Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Automat. Control. 26(1), 17\u201332 (1981)","journal-title":"IEEE Trans. Automat. Control."},{"issue":"2","key":"3309_CR45","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1080\/03772063.2015.1075915","volume":"62","author":"A Narwal","year":"2015","unstructured":"A. Narwal, B.R. Prasad, A novel order reduction approach for LTI systems using cuckoo search optimization and stability equation. IETE J. Res. 62(2), 154\u2013163 (2015). https:\/\/doi.org\/10.1080\/03772063.2015.1075915","journal-title":"IETE J. Res."},{"key":"3309_CR46","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-023-09489-8","author":"AP Padhy","year":"2024","unstructured":"A.P. Padhy, S. Panigrahi, V.P. Singh, Model order reduction for SISO and MIMO system using improved adaptive differential evolution algorithm. Soft. Comput. (2024). https:\/\/doi.org\/10.1007\/s00500-023-09489-8","journal-title":"Soft. Comput."},{"key":"3309_CR47","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1007\/s00422-021-00888-4","volume":"115","author":"A Padoan","year":"2021","unstructured":"A. Padoan, F. Forni, R. Sepulchre, Balanced truncation for model reduction of biological oscillators. Biol. Cybern. 115, 383\u2013395 (2021). https:\/\/doi.org\/10.1007\/s00422-021-00888-4","journal-title":"Biol. Cybern."},{"key":"3309_CR48","first-page":"22","volume":"5","author":"S Panda","year":"2009","unstructured":"S. Panda, J.S. Yadav, N.P. Padidar, C. Ardil, Evolutionary techniques for model order reduction of large-scale linear systems. Int. J. Appl. Sci. Eng. Technol. 5, 22\u201328 (2009)","journal-title":"Int. J. Appl. Sci. Eng. Technol."},{"key":"3309_CR49","first-page":"73","volume":"1","author":"G Parmar","year":"2007","unstructured":"G. Parmar, S. Mukherjee, R. Prasad, Reduced order modelling of linear dynamic systems using particle swarm optimized eigen spectrum analysis. Int. J. Electr. Comput. Eng. 1, 73\u201380 (2007)","journal-title":"Int. J. Electr. Comput. Eng."},{"issue":"11","key":"3309_CR50","doi-asserted-by":"publisher","first-page":"2542","DOI":"10.1016\/j.apm.2006.10.004","volume":"31","author":"G Parmar","year":"2007","unstructured":"G. Parmar, S. Mukherjee, R. Prasad, System reduction using factor division algorithm and Eigen spectrum analysis. Appl. Math. Model. 31(11), 2542\u20132552 (2007)","journal-title":"Appl. Math. Model."},{"key":"3309_CR51","doi-asserted-by":"publisher","unstructured":"G. Parmar, M.K. Pandey, V. Kumar. System order reduction using GA for unit impulse input and a comparative study using ISE and IRE, in: 9th International Conference on Adv. in Comp., Comm. and Control, Mumbai, pp 1\u20137, 2009, https:\/\/doi.org\/10.1145\/1523103.1523105","DOI":"10.1145\/1523103.1523105"},{"issue":"2","key":"3309_CR52","first-page":"244","volume":"1","author":"G Parmar","year":"2007","unstructured":"G. Parmar, R. Prasad, S. Mukherjee, Order reduction of linear dynamic systems using stability equation method and GA. Int. J. Electr. Comput. Eng. 1(2), 244\u2013250 (2007)","journal-title":"Int. J. Electr. Comput. Eng."},{"issue":"3","key":"3309_CR53","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12046-021-01647-8","volume":"46","author":"SR Potturu","year":"2021","unstructured":"S.R. Potturu, R. Prasad, R. Meshram, Improved simplification technique for LTI systems using modified time moment matching method. Sadhana 46(3), 1\u201311 (2021)","journal-title":"Sadhana"},{"key":"3309_CR54","doi-asserted-by":"publisher","first-page":"1497","DOI":"10.1007\/s00034-021-01860-0","volume":"41","author":"AK Prajapati","year":"2022","unstructured":"A.K. Prajapati, R. Prasad, A new generalized pole clustering-based model reduction technique and its application for design of controllers. Circuits Syst. Signal Process. 41, 1497\u20131529 (2022). https:\/\/doi.org\/10.1007\/s00034-021-01860-0","journal-title":"Circuits Syst. Signal Process."},{"issue":"2","key":"3309_CR55","doi-asserted-by":"publisher","first-page":"1682","DOI":"10.1080\/03772063.2022.2163929","volume":"70","author":"AK Prajapati","year":"2023","unstructured":"A.K. Prajapati, R. Prasad, A new model reduction technique for the simplification and controller design of large-scale systems. IETE J. Res. 70(2), 1682\u20131698 (2023). https:\/\/doi.org\/10.1080\/03772063.2022.2163929","journal-title":"IETE J. Res."},{"issue":"5","key":"3309_CR56","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1080\/02564602.2018.1503567","volume":"36","author":"AK Prajapati","year":"2018","unstructured":"A.K. Prajapati, R. Prasad, Reduced order modelling of linear time invariant systems using the factor division method to allow retention of dominant modes. IETE Tech. Rev. 36(5), 449\u2013462 (2018). https:\/\/doi.org\/10.1080\/02564602.2018.1503567","journal-title":"IETE Tech. Rev."},{"issue":"7","key":"3309_CR57","doi-asserted-by":"publisher","first-page":"1177","DOI":"10.1016\/j.jfranklin.2009.10.016","volume":"348","author":"R Salim","year":"2011","unstructured":"R. Salim, M. Bettayeb, H2 and H\u221e optimal model reduction using genetic algorithms. J. Frankl. Inst. 348(7), 1177\u20131191 (2011). https:\/\/doi.org\/10.1016\/j.jfranklin.2009.10.016","journal-title":". Frankl. Inst."},{"key":"3309_CR58","doi-asserted-by":"publisher","unstructured":"U. Salma, K. Vaisakh, Reduced order modeling of linear MIMO systems using soft computing techniques, ed. by B.K. Panigrahi, P.N. Suganthan, S. Das, S.C. Satapathy, Swarm, Evolutionary, and Memetic Computing. SEMCCO 2011. Lecture Notes in Computer Science, vol. 7077 (Springer, Berlin, 2011). https:\/\/doi.org\/10.1007\/978-3-642-27242-4_32","DOI":"10.1007\/978-3-642-27242-4_32"},{"issue":"no. 6","key":"3309_CR59","doi-asserted-by":"publisher","first-page":"2022","DOI":"10.1109\/TCSII.2020.3038715","volume":"68","author":"ER Samuel","year":"2021","unstructured":"E.R. Samuel, K.K. Deveerasetty, Laguerre expansion series based reduced order interval systems. IEEE Trans. Circ. Syst. II Express Briefs 68(6), 2022\u20132026 (2021). https:\/\/doi.org\/10.1109\/TCSII.2020.3038715","journal-title":"IEEE Trans. Circ. Syst. II Express Briefs"},{"issue":"5","key":"3309_CR60","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1109\/TAC.1974.1100661","volume":"19","author":"Y Shamash","year":"1974","unstructured":"Y. Shamash, Stable reduced-order models using Pad\u00e9-type approximations. IEEE Trans. Automat. Control. 19(5), 615\u2013616 (1974). https:\/\/doi.org\/10.1109\/TAC.1974.1100661","journal-title":"IEEE Trans. Automat. Control."},{"issue":"2","key":"3309_CR61","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1080\/03772063.2015.1009396","volume":"61","author":"A Sikander","year":"2015","unstructured":"A. Sikander, B.R. Prasad, A novel order reduction method using cuckoo search algorithm. IETE J. Res. 61(2), 83\u201390 (2015). https:\/\/doi.org\/10.1080\/03772063.2015.1009396","journal-title":"IETE J. Res."},{"key":"3309_CR62","doi-asserted-by":"publisher","first-page":"3471","DOI":"10.1007\/s00034-015-0018-4","volume":"34","author":"A Sikander","year":"2015","unstructured":"A. Sikander, R. Prasad, Soft computing approach for model order reduction of linear time invariant systems. Circ. Syst. Signal Process. 34, 3471\u20133487 (2015)","journal-title":"Circ. Syst. Signal Process."},{"issue":"16","key":"3309_CR63","doi-asserted-by":"publisher","first-page":"4848","DOI":"10.1016\/j.apm.2015.04.014","volume":"39","author":"A Sikander","year":"2015","unstructured":"A. Sikander, R. Prasad, Linear time-invariant system reduction using a mixed methods approach. Appl. Math. Model. 39(16), 4848\u20134858 (2015)","journal-title":"Appl. Math. Model."},{"issue":"9","key":"3309_CR64","doi-asserted-by":"publisher","first-page":"1453","DOI":"10.1007\/s12046-017-0710-0","volume":"42","author":"A Sikander","year":"2017","unstructured":"A. Sikander, R. Prasad, New technique for system simplification using Cuckoo search and ESA. Sadhana 42(9), 1453\u20131458 (2017)","journal-title":"Sadhana"},{"key":"3309_CR65","doi-asserted-by":"publisher","DOI":"10.1080\/03772063.2016.1272436","author":"A Sikander","year":"2017","unstructured":"A. Sikander, R. Prasad, A new technique for reduced-order modelling of linear time-invariant system. IETE J. Res. (2017). https:\/\/doi.org\/10.1080\/03772063.2016.1272436","journal-title":"IETE J. Res."},{"issue":"10","key":"3309_CR66","doi-asserted-by":"publisher","first-page":"3449","DOI":"10.1007\/s00500-017-2589-4","volume":"22","author":"A Sikander","year":"2018","unstructured":"A. Sikander, P. Thakur, Reduced order modelling of linear time-invariant system using modified cuckoo search algorithm. Soft. Comput. 22(10), 3449\u20133459 (2018)","journal-title":"Soft. Comput."},{"issue":"no. 3","key":"3309_CR67","doi-asserted-by":"publisher","first-page":"4598","DOI":"10.1109\/TIA.2024.3354895","volume":"60","author":"VP Singh","year":"2024","unstructured":"V.P. Singh, U.K. Yadav, V.P. Meena, A.V. Waghmare, A. Gupta, B. Pratap, Proximity index value based systematized approximation of higher-order interconnected power system model. IEEE Trans. Ind. Appl. 60(3), 4598\u20134607 (2024). https:\/\/doi.org\/10.1109\/TIA.2024.3354895","journal-title":"IEEE Trans. Ind. Appl."},{"issue":"3","key":"3309_CR68","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/0045-7906(90)90020-G","volume":"16","author":"AK Sinha","year":"1990","unstructured":"A.K. Sinha, J. Pal, Simulation based reduced order modelling using a clustering technique. Comput. Electr. Eng. 16(3), 159\u2013169 (1990)","journal-title":"Comput. Electr. Eng."},{"issue":"7","key":"3309_CR69","doi-asserted-by":"publisher","first-page":"1449","DOI":"10.1007\/s11538-017-0277-2","volume":"79","author":"TJ Snowden","year":"2017","unstructured":"T.J. Snowden, P.H. Vander Graaf, M.J. Tindall, Methods of model reduction for large-scale biological systems: a survey of current methods and trends. Bull. Math. Biol. 79(7), 1449\u20131486 (2017)","journal-title":"Bull. Math. Biol."},{"issue":"3","key":"3309_CR70","doi-asserted-by":"publisher","first-page":"41","DOI":"10.13189\/ujca.2020.080301","volume":"8","author":"SK Suman","year":"2020","unstructured":"S.K. Suman, A. Kumar, Model reduction of power system by modified balanced truncation method. Univ. J. Control Autom. (Cease Publication) 8(3), 41\u201352 (2020). https:\/\/doi.org\/10.13189\/ujca.2020.080301","journal-title":"Univ. J. Control Autom. (Cease Publication)"},{"key":"3309_CR71","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1016\/j.jfluidstructs.2017.03.004","volume":"71","author":"S Timme","year":"2017","unstructured":"S. Timme, K.J. Badcock, A. Da Ronch, Gust analysis using computational fluid dynamics derived reduced order models. J. Fluids Struct. 71, 116\u2013125 (2017). https:\/\/doi.org\/10.1016\/j.jfluidstructs.2017.03.004","journal-title":"J. Fluids Struct."},{"issue":"1","key":"3309_CR72","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1007\/s40313-016-0282-y","volume":"28","author":"SK Tiwari","year":"2017","unstructured":"S.K. Tiwari, G. Kaur, Model reduction by new clustering method and frequency response matching. J. Control Autom. Electr. Syst. 28(1), 78\u201385 (2017)","journal-title":"J. Control Autom. Electr. Syst."},{"issue":"5","key":"3309_CR73","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TMAG.2022.3232701","volume":"59","author":"M Tobita","year":"2023","unstructured":"M. Tobita, T. Matsuo, Nonlinear model order reduction of a variable reluctance stepper motor using the parameterized Cauer ladder network method. IEEE Trans. Magnet. 59(5), 1\u20134 (2023). https:\/\/doi.org\/10.1109\/TMAG.2022.3232701","journal-title":"IEEE Trans. Magnet."},{"key":"3309_CR74","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1016\/j.apm.2021.04.017","volume":"97","author":"G Vasu","year":"2021","unstructured":"G. Vasu, M.S. Kumar, M.R. Raju, Internal model control design based on approximation of linear discrete dynamical systems. Appl. Math. Model. 97, 683\u2013700 (2021). https:\/\/doi.org\/10.1016\/j.apm.2021.04.017","journal-title":"Appl. Math. Model."},{"issue":"2","key":"3309_CR75","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1177\/0959651819849372","volume":"234","author":"G Vasu","year":"2020","unstructured":"G. Vasu, M. Sivakumar, M. Ramalingaraju, A novel model reduction approach for linear time-invariant systems via enhanced PSO-DV algorithm and improved MPPA method. Proc. Inst. Mech. Eng. I J. Syst. Control Eng. 234(2), 240\u2013256 (2020). https:\/\/doi.org\/10.1177\/0959651819849372","journal-title":"Proc. Inst. Mech. Eng. I J. Syst. Control Eng."},{"issue":"1","key":"3309_CR76","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1177\/0142331220921578","volume":"43","author":"G Vasu","year":"2021","unstructured":"G. Vasu, M. Sivakumar, M. Ramalingaraju, Optimal IMC-PID controller design for large-scale power systems via EDE algorithm-based model approximation method. Trans. Inst. Meas. Control. 43(1), 59\u201377 (2021)","journal-title":"Trans. Inst. Meas. Control."},{"issue":"3","key":"3309_CR77","doi-asserted-by":"publisher","first-page":"1039","DOI":"10.1007\/s00034-012-9483-1","volume":"32","author":"Q Wang","year":"2013","unstructured":"Q. Wang, Y. Wang, E.Y. Lam, N. Wong, Model order reduction for neutral systems by moment matching. Circ. Syst. Signal Process. 32(3), 1039\u20131063 (2013)","journal-title":"Circ. Syst. Signal Process."},{"issue":"6","key":"3309_CR78","doi-asserted-by":"publisher","first-page":"1161","DOI":"10.1049\/piee.1970.0227","volume":"117","author":"DA Wilson","year":"1970","unstructured":"D.A. Wilson, Optimal solution of model reduction problem. Proc. Inst. Electr. Eng. 117(6), 1161\u20131165 (1970)","journal-title":"Proc. Inst. Electr. Eng."},{"key":"3309_CR79","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1080\/00207177408932715","volume":"20","author":"DA Wilson","year":"1974","unstructured":"D.A. Wilson, Model reduction for multivariable systems. Int. J. Control. 20, 57\u201364 (1974)","journal-title":"Int. J. Control."},{"issue":"11","key":"3309_CR80","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TMAG.2023.3300996","volume":"59","author":"K Xu","year":"2023","unstructured":"K. Xu, Y. Guo, G. Lei, X. Sun, J. Zhu, Electromagnetic performance analysis of a bearingless permanent magnet synchronous motor by model order reduction. IEEE Trans. Magn. 59(11), 1\u20135 (2023). https:\/\/doi.org\/10.1109\/TMAG.2023.3300996","journal-title":"IEEE Trans. Magn."},{"issue":"1","key":"3309_CR81","doi-asserted-by":"publisher","first-page":"2052","DOI":"10.1109\/TPWRS.2023.3270366","volume":"39","author":"Z Zhao","year":"2024","unstructured":"Z. Zhao, J. Wu, X. Luo, J. Xie, Q. Yang, Q. Ni, Reduced-order model for wind-solar multi-microgrids considering time-scale coupling. IEEE Trans. Power Syst. 39(1), 2052\u20132065 (2024). https:\/\/doi.org\/10.1109\/TPWRS.2023.3270366","journal-title":"IEEE Trans. Power Syst."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-025-03309-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-025-03309-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-025-03309-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T09:13:49Z","timestamp":1774602829000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-025-03309-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,9]]},"references-count":81,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["3309"],"URL":"https:\/\/doi.org\/10.1007\/s00034-025-03309-0","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,9]]},"assertion":[{"value":"8 February 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 August 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 August 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 September 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors (s) declare no potential conflicts of interest with respect to the research, authorship, and\/or publication of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}