https://orcid.org/0000-0003-1098-275X
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Abstract
The problem of input–output stability analysis and stabilisation of discrete Takagi–Sugeno (T–S) fuzzy systems with a time-varying delay via an input–output (I–O) approach is investigated in this paper. Using a three-term approximation-based model, a forward subsystem with three constant delays and a feedback subsystem are presented. Two separate input–output stability criteria have been formulated, using an input–output approach and a scaled small gain theorem: a criterion based on the lifting method, a non-quadratic Lyapunov function, and bounded real lemma, another criterion based on a non-quadratic Lyapunov–krasovskii functional approach. Using this result, the input–output stabilisation problem is resolved through the so-called parallel distributed compensation (PDC) scheme. The conditions obtained are presented in terms of linear matrix inequalities (LMIs). Three numerical examples are provided to demonstrate the advantages and merit of the proposed method.
Acknowledgments
Hicham El Aiss has been supported by Fondo Nacional de Desarrollo Cientfico y Tecnologico-Fondecyt, Chile, under grant No: 3190378.
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No potential conflict of interest was reported by the author(s).
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Notes on contributors
Hicham El Aiss
Hicham El Aiss received his master's degree in signals systems and informatics from the University of Sidi Mohamed Ben Abdelah, faculty of sciences in 2013, received his Ph.D degree in Electrical Engineering from the same university in 2018. He is currently a post-doc position in University of Santiago, Chile, under grant N:3190378. His current research interests include delay systems, stability theory, robust control, fuzzy control, vehicle dynamics and descriptor systems.
Redouane Chaibi
Redouane Chaibi, received the Master in Signals Systems and Computing from University of Sidi Mohammed Ben Abdellah, Faculty of Sciences, Fez, Morocco in 2014. He is a Ph.D. student in the same Faculty. His research interests include stability and stabilization of T-S fuzzy system.
Ahmed El Hajjaji
Ahmed El Hajjaji, received his Ph.D in automatic control from the University Of Picardie Jules vernes, France in 1993. He was an associate Professor in the same University from 1994 to 2003. He is currently a full Professor in the same University. Since 2001, he has also been the head of the research team of control and vehicle of modeling, information and systems (MIS) laboratory. His current research interests include fuzzy control, vehicle dynamics, fault-tolerant control, neural networks, manglev systems and renewable energy systems.
Abdelaziz Hmamed
Abdelaziz Hmamed, was born in sefrou, morocco, in 1951. He received the doctorate of state degree in electrical engineering from the Faculty of Sciences, Rabat, Morocco, in 1985. Since 1986 he has been with the department of Physics, Faculty Of Sciences Dhar El Mehraz at Fez, where he is currently a full Professor. His research interests are delay systems, stability theory, systems with constraints and 2-D systems.