{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T07:31:06Z","timestamp":1771659066327,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,16]],"date-time":"2020-11-16T00:00:00Z","timestamp":1605484800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This article proposes a new nonlinear state-feedback stability controller utilizing linear matrix inequality (LMI) for time-delay nonlinear systems in the presence of Lipschitz nonlinearities and subject to parametric uncertainties. Following the Lyapunov\u2013Krasovskii stabilization scheme, the asymptotic stability criterion resulted in the LMI form and the nonlinear state-feedback control technique was determined. Due to their significant contributions to the system stability, time delays and system uncertainties were taken into account while the suggested scheme was designed so that the system\u2019s stabilization was satisfied in spite of time delays and system uncertainties. The benefit of the proposed method is that not only is the control scheme independent of the system order, but it is also fairly simple. Hence, there is no complexity in using the proposed technique. Finally, to justify the proficiency and performance of the suggested technique, a numerical system and a rotational inverted pendulum were studied. Numerical simulations and experimental achievements prove the efficiency of the suggested control technique.<\/jats:p>","DOI":"10.3390\/sym12111883","type":"journal-article","created":{"date-parts":[[2020,11,16]],"date-time":"2020-11-16T22:48:47Z","timestamp":1605566927000},"page":"1883","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["An LMI Approach to Nonlinear State-Feedback Stability of Uncertain Time-Delay Systems in the Presence of Lipschitzian Nonlinearities"],"prefix":"10.3390","volume":"12","author":[{"given":"Mehdi","family":"Golestani","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Iran University of Science and Technology, Tehran 16844, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5676-1875","authenticated-orcid":false,"given":"Saleh","family":"Mobayen","sequence":"additional","affiliation":[{"name":"Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7475-4628","authenticated-orcid":false,"given":"S. Hassan","family":"HosseinNia","sequence":"additional","affiliation":[{"name":"Department of Precision and Microsystems Engineering, Delft University of Technology, 2628CD Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saeed","family":"Shamaghdari","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Iran University of Science and Technology, Tehran 16844, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1002\/cplx.21695","article-title":"Optimal LMI-based state feedback stabilizer for uncertain nonlinear systems with time-Varying uncertainties and disturbances","volume":"21","author":"Mobayen","year":"2016","journal-title":"Complexity"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Huo, Y., and Liu, J.-B. (2019). Robust H\u221e Control For Uncertain Singular Neutral Time-Delay Systems. Mathematics, 7.","DOI":"10.3390\/math7030217"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Emharuethai, C., Niamsup, P., Ramachandran, R., and Weera, W. (2020). Time-Varying Delayed H\u221e Control Problem for Nonlinear Systems: A Finite Time Study Using Quadratic Convex Approach. Symmetry, 12.","DOI":"10.3390\/sym12050713"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Yao, H. (2019). Anti-Saturation Control of Uncertain Time-Delay Systems with Actuator Saturation Constraints. Symmetry, 11.","DOI":"10.3390\/sym11030375"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5308","DOI":"10.1016\/j.jfranklin.2015.09.003","article-title":"Output feedback stabilization for high-order uncertain feedforward time-delay nonlinear systems","volume":"352","author":"Sun","year":"2015","journal-title":"J. Frankl. Inst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Puangmalai, W., Puangmalai, J., and Rojsiraphisal, T. (2020). Robust Finite-Time Control of Linear System with Non-Differentiable Time-Varying Delay. Symmetry, 12.","DOI":"10.3390\/sym12040680"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"30951","DOI":"10.1109\/ACCESS.2019.2902567","article-title":"A survey of recent advances in fractional order control for time delay systems","volume":"7","author":"Birs","year":"2019","journal-title":"IEEE Access"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.automatica.2019.01.004","article-title":"Globally adaptive control for stochastic nonlinear time-delay systems with perturbations and its application","volume":"102","author":"Min","year":"2019","journal-title":"Automatica"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ruan, Y., and Huang, T. (2020). Finite-Time Control for Nonlinear Systems with Time-Varying Delay and Exogenous Disturbance. Symmetry, 12.","DOI":"10.3390\/sym12030447"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1002\/asjc.895","article-title":"Adaptive control design for a class of uncertain high-order nonlinear systems with time delay","volume":"17","author":"Sun","year":"2015","journal-title":"Asian J. Control"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1514","DOI":"10.1002\/rnc.3155","article-title":"H\u221e observer design for uncertain nonlinear discrete-time systems with time-delay: LMI optimization approach","volume":"25","author":"Sayyaddelshad","year":"2015","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1186\/1687-1847-2012-180","article-title":"Exponential stabilization of uncertain nonlinear time-delay systems","volume":"2012","author":"Dong","year":"2012","journal-title":"Adv. Differ. Equ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1007\/s11633-010-0236-y","article-title":"Adaptive fuzzy observer backstepping control for a class of uncertain nonlinear systems with unknown time-delay","volume":"7","author":"Tong","year":"2010","journal-title":"Int. J. Autom. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1016\/j.nahs.2010.02.002","article-title":"Robust H\u221e control for uncertain T\u2013S fuzzy time-delay systems with sampled-data input and nonlinear perturbations","volume":"4","author":"Lien","year":"2010","journal-title":"Nonlinear Anal. Hybrid Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1080\/00207170903377119","article-title":"Output feedback stabilisation for uncertain nonlinear time-delay systems subject to input constraints","volume":"83","author":"Goodall","year":"2010","journal-title":"Int. J. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1808","DOI":"10.1016\/j.jfranklin.2012.02.009","article-title":"Stabilization of discrete-time switched singular time-delay systems under asynchronous switching","volume":"349","author":"Lin","year":"2012","journal-title":"J. Frankl. Inst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s11071-014-1862-7","article-title":"A new stability result for nonlinear cascade time-delay system and its application in chaos control","volume":"80","author":"Wang","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1016\/j.ijepes.2018.12.026","article-title":"Chance-constrained stochastic congestion management of power systems considering uncertainty of wind power and demand side response","volume":"107","author":"Wu","year":"2019","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wang, X., and Hou, B. (2020). Continuous time-varying feedback control of a robotic manipulator with base vibration and load uncertainty. J. Vib. Control, 1077546320927598.","DOI":"10.1177\/1077546320927598"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"8735","DOI":"10.1007\/s00521-019-04373-9","article-title":"Asymptotic tracking control of uncertain nonholonomic wheeled mobile robot with actuator saturation and external disturbances","volume":"32","author":"Wu","year":"2020","journal-title":"Neural Comput. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1806","DOI":"10.1016\/j.automatica.2007.10.039","article-title":"Adaptive task-space regulation of rigid-link flexible-joint robots with uncertain kinematics","volume":"44","author":"Liu","year":"2008","journal-title":"Automatica"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.sysconle.2004.08.010","article-title":"Robust H2 filtering for uncertain linear systems: LMI based methods with parametric Lyapunov functions","volume":"54","author":"Barbosa","year":"2005","journal-title":"Syst. Control Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1657","DOI":"10.1002\/rnc.1313","article-title":"Robust fault estimation of uncertain systems using an LMI-based approach","volume":"18","author":"Nobrega","year":"2008","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.ejcon.2015.01.007","article-title":"Sufficient LMI conditions for reduced-order multi-objective H2\/H\u221e control of LTI systems","volume":"23","author":"Hilhorst","year":"2015","journal-title":"Eur. J. Control"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2898","DOI":"10.1016\/j.jfranklin.2011.09.012","article-title":"H2 optimal semistable control for linear dynamical systems: An LMI approach","volume":"348","author":"Haddad","year":"2011","journal-title":"J. Frankl. Inst."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Guerrero-S\u00e1nchez, M.-E., Hern\u00e1ndez-Gonz\u00e1lez, O., Lozano, R., Garc\u00eda-Beltr\u00e1n, C.-D., Valencia-Palomo, G., and L\u00f3pez-Estrada, F.-R. (2019). Energy-Based Control and LMI-Based Control for a Quadrotor Transporting a Payload. Mathematics, 7.","DOI":"10.3390\/math7111090"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Li, L., and Liao, F. (2020). Preview Control for MIMO Discrete-Time System with Parameter Uncertainty. Mathematics, 8.","DOI":"10.3390\/math8050756"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1287","DOI":"10.1016\/j.nahs.2008.09.018","article-title":"Robust H\u221e stabilization for uncertain switched impulsive control systems with state delay: An LMI approach","volume":"2","author":"Zong","year":"2008","journal-title":"Nonlinear Anal. Hybrid Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1093\/imamci\/dnp018","article-title":"Robust \u210b\u221e state feedback control of discrete-time systems with state delay: An LMI approach","volume":"26","author":"Leite","year":"2009","journal-title":"IMA J. Math. Control Inf."},{"key":"ref_30","unstructured":"Tsai, S.-H., Hsiao, M.-Y., Li, T.-H.S., Shih, K.-S., Chao, C.-H., and Liu, C.-H. (2009, January 11\u201314). LMI-based H\u221e state-feedback control for TS time-delay discrete fuzzy bilinear system. Proceedings of the 2009 IEEE International Conference on Systems, Man and Cybernetics, San Antonio, TX, USA."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1016\/j.chaos.2007.08.059","article-title":"Delay-dependent robust BIBO stabilization of uncertain system via LMI approach","volume":"40","author":"Li","year":"2009","journal-title":"Chaos Solitons Fractals"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Amri, I., Soudani, D., and Benrejeb, M. (2011, January 3\u20135). Robust state-derivative feedback LMI-based designs for time-varying delay system. Proceedings of the 2011 International Conference on Communications, Computing and Control Applications (CCCA), Hammamet, Tunisia.","DOI":"10.1109\/CCCA.2011.6031530"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1100","DOI":"10.1007\/s11424-011-8360-5","article-title":"Stabilization of Euler-Bernoulli beam with a nonlinear locally distributed feedback control","volume":"24","author":"Yan","year":"2011","journal-title":"J. Syst. Sci. Complex."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1051\/cocv\/2009028","article-title":"Nonlinear feedback stabilization of a two-dimensional Burgers equation","volume":"16","author":"Thevenet","year":"2010","journal-title":"ESAIM Control Optim. Calc. Var."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/0167-6911(87)90102-2","article-title":"A stabilization algorithm for a class of uncertain linear systems","volume":"8","author":"Petersen","year":"1987","journal-title":"Syst. Control Lett."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM.","DOI":"10.1137\/1.9781611970777"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1786","DOI":"10.1016\/j.nonrwa.2010.11.011","article-title":"Stabilization and tracking control for a class of nonlinear systems","volume":"12","author":"Rehan","year":"2011","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1007\/s11071-015-1892-9","article-title":"An ISM-based CNF tracking controller design for uncertain MIMO linear systems with multiple time-delays and external disturbances","volume":"80","author":"Majd","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1016\/j.amc.2008.05.150","article-title":"Novel LMI conditions for observer-based stabilization of Lipschitzian nonlinear systems and uncertain linear systems in discrete-time","volume":"206","author":"Ibrir","year":"2008","journal-title":"Appl. Math. Comput."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/11\/1883\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:34:06Z","timestamp":1760178846000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/11\/1883"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,16]]},"references-count":39,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["sym12111883"],"URL":"https:\/\/doi.org\/10.3390\/sym12111883","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,16]]}}}