{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T16:23:17Z","timestamp":1769012597305,"version":"3.49.0"},"reference-count":26,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,8,29]],"date-time":"2022-08-29T00:00:00Z","timestamp":1661731200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Deanship at the University of Ha\u2019il\u2014Saudi Arabia","award":["RG-21 159"],"award-info":[{"award-number":["RG-21 159"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The challenge of developing observers for classical integer-order systems that are both resilient and non-fragile has received a lot of attention in the literature. However, only a few articles have addressed the topic of developing observers for Fractional-Order (FO) systems that are both H-infinity H\u221e and non-fragile. The current work handles the Caputo fractional-order systems as the first work, to our knowledge, which treats such problems. The authors provide a novel result for building non-fragile and robust observers for nonlinear Caputo fractional-order systems. For this, the H\u221e performance method is utilized. Simulations for a numerical example confirm the efficacy of the suggested technique. The primary advantage of the current work is that it is the first to address the Caputo fractional-order system problem.<\/jats:p>","DOI":"10.3390\/sym14091795","type":"journal-article","created":{"date-parts":[[2022,8,31]],"date-time":"2022-08-31T02:09:36Z","timestamp":1661911776000},"page":"1795","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Robust and Non-Fragile Observer Design for Nonlinear Fractional-Order Systems"],"prefix":"10.3390","volume":"14","author":[{"given":"Omar","family":"Kahouli","sequence":"first","affiliation":[{"name":"Department of Electronics Engineering, Community College, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"},{"name":"Control and Energy Management Laboratory, National School of Engineering, Sfax University, BP 1173, Sfax 3038, Tunisia"}]},{"given":"Omar","family":"Naifar","sequence":"additional","affiliation":[{"name":"Control and Energy Management Laboratory, National School of Engineering, Sfax University, BP 1173, Sfax 3038, Tunisia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7142-7026","authenticated-orcid":false,"given":"Abdellatif Ben","family":"Makhlouf","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jouf University, Sakaka 72311, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8785-3513","authenticated-orcid":false,"given":"Yassine","family":"Bouteraa","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, College of Computer Engineering and Sciences, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"}]},{"given":"Ali","family":"Aloui","sequence":"additional","affiliation":[{"name":"Department of Electronics Engineering, Community College, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"}]},{"given":"Ali","family":"Rebhi","sequence":"additional","affiliation":[{"name":"Department of Electronics Engineering, Community College, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Monje, C.A., Chen, Y., Vinagre, B.M., Xue, D., and Feliu-Batlle, V. (2010). Fractional Order Systems and Controls: Fundamentals and Applications, Springer.","DOI":"10.1007\/978-1-84996-335-0"},{"key":"ref_2","unstructured":"Walterde Gruyter, K.G. (2015). Fractional Dynamics, De Gruyter Open Poland."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2033","DOI":"10.1002\/mma.6909","article-title":"Henry\u2013Gronwall type q-fractional integral inequalities","volume":"44","author":"Makhlouf","year":"2021","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"106270","DOI":"10.1016\/j.cnsns.2022.106270","article-title":"Stability analysis of time-delay incommensurate fractional-order systems","volume":"109","author":"Mohammad","year":"2022","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.fss.2021.06.013","article-title":"Finite-time fuzzy reliable controller design for fractional-order tumor system under chemotherapy","volume":"432","author":"Dhanalakshmi","year":"2022","journal-title":"Fuzzy Sets Syst."},{"key":"ref_6","unstructured":"Majid, G. (2022). Robust stabilization criteria of a general form of fractional-order controllers for interval fractional-order plants with complex uncertain parameters. ISA Trans., in press."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s11063-021-10631-6","article-title":"Pseudo-State Estimation for Fractional Order Neural Networks","volume":"54","author":"Wang","year":"2022","journal-title":"Neural Process. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2568","DOI":"10.1109\/TCYB.2017.2655501","article-title":"Observer-based fuzzy adaptive output-feedback control of stochastic nonlinear multiple time-delay systems","volume":"47","author":"Wang","year":"2017","journal-title":"IEEE Trans. Cybern."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1007\/s00170-016-9351-4","article-title":"A nonlinear Takagi-Sugeno fuzzy logic control for single machine power system","volume":"90","author":"Salah","year":"2017","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"112388","DOI":"10.1016\/j.chaos.2022.112388","article-title":"Nonlinear biological population model; computational and numerical investigations","volume":"162","author":"Mostafa","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1007\/s11082-022-04007-w","article-title":"Recent electronic communications; optical quasi\u2013monochromatic soliton waves in fiber medium of the perturbed Fokas\u2013Lenells equation","volume":"54","author":"Khater","year":"2022","journal-title":"Opt. Quantum Electron."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, R., Xing, J., Wang, P., and Yang, Q. (2012, January 3\u20135). Non-Fragile Observer Design for Nonlinear Switched Time Delay Systems Using Delta Operator. Proceedings of the IEEE 2012 UKACC International Conference on Control, Cardiff, UK.","DOI":"10.1109\/CONTROL.2012.6334661"},{"key":"ref_13","first-page":"606","article-title":"Non-fragile Observer Design and Stabilization Control for Singular Systems","volume":"36","author":"Xiao","year":"2012","journal-title":"J. Nanjing Univ. Sci. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1806","DOI":"10.1002\/rnc.1785","article-title":"H\u221e sliding mode observer design for a class of nonlinear discrete time-delay systems: A delay-fractioning approach","volume":"22","author":"Hu","year":"2012","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.automatica.2015.10.052","article-title":"New unified H\u221e dynamic observer design for linear systems with unknown inputs","volume":"65","author":"Gao","year":"2016","journal-title":"Automatica"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1659","DOI":"10.1109\/TMECH.2016.2522759","article-title":"H\u221e Observer Design for LPV Systems With Uncertain Measurements on Scheduling Variables: Application to an Electric Ground Vehicle","volume":"21","author":"Zhang","year":"2016","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.sigpro.2014.02.021","article-title":"Fractional model of an electrochemical capacitor","volume":"107","author":"Martynyuk","year":"2015","journal-title":"Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Atangana, A., and Baleanu, D. (2016). New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model. arXiv.","DOI":"10.2298\/TSCI160111018A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.isatra.2021.03.033","article-title":"An ADRC-based backstepping control design for a class of fractional-order systems","volume":"121","author":"Fatemeh","year":"2022","journal-title":"ISA Trans."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"109962","DOI":"10.1016\/j.automatica.2021.109962","article-title":"Basin, Bounded real lemma for singular linear continuous-time fractional-order systems","volume":"135","author":"Saliha","year":"2022","journal-title":"Automatica"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1801","DOI":"10.1007\/s11071-014-1889-9","article-title":"An iterative method to design optimal non-fragile H\u221e observer for Lipschitz nonlinear fractional-order systems","volume":"80","author":"Boroujeni","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s10440-020-00323-z","article-title":"Mixed H\u221e $ H_ {\\infty} $ and Passive Control for Fractional-Order Nonlinear Systems Via LMI Approach","volume":"170","author":"Huong","year":"2020","journal-title":"Acta Appl. Math."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"650","DOI":"10.1016\/j.cnsns.2014.10.008","article-title":"Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems","volume":"22","author":"Gallegos","year":"2015","journal-title":"Commun. Nonlinear Sci. Numer. Simulat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1965","DOI":"10.1016\/j.automatica.2009.04.003","article-title":"Mittag-Leffler stability of fractional order nonlinear dynamic systems","volume":"45","author":"Li","year":"2009","journal-title":"Automatica"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhang, F. (2006). The Schur Complement and Its Applications, Springer Science & Business Media.","DOI":"10.1007\/b105056"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Naifar, O., Jmal, A., and Ben Makhlouf, A. (2021). Non-fragile H\u221e observer for Lipschitz conformable fractional-order systems. Asian J. Control.","DOI":"10.1007\/978-3-030-71446-8_4"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/9\/1795\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:19:33Z","timestamp":1760141973000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/9\/1795"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,29]]},"references-count":26,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["sym14091795"],"URL":"https:\/\/doi.org\/10.3390\/sym14091795","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,29]]}}}