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Stability Analysis and Robust H∞ Controller Synthesis with Derivatives of Membership Functions for T-S Fuzzy Systems with Time-varying Delay: Input-output Stability Approach

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Abstract

This paper investigates the problem of delay dependent stability and H∞ control design with derivatives of membership functions of uncertain Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. A model transformation is employed by considering a three-term approximation of delayed state vector. Using Scaled Small Gain (SSG) theorem and fuzzy weighting-dependent Lyapunov functions with some useful slack variables, less conservative robust stability and stabilization criteria are formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by using standard numerical packages. Finally, numerical experiments are presented to illustrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. Department of Physics Faculty of Sciences Dhar El Mehraz, B.P. 1796, Fes-Atlas, Morocco

    Redouane Chaibi, Hicham El Aiss & Abdelaziz Hmamed

  2. Laboratoire Modelisation, Information and Systems, University of Picardie Jules Verne, 7, Rue moulin Neuf, 80000, Amiens, France

    Ahmed El Hajjaji

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  1. Redouane Chaibi
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  2. Hicham El Aiss
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Correspondence to Redouane Chaibi.

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Redouane Chaibi received his Master’s degree in Signals Systems and Computing from University of Sidi Mohammed Ben Abdellah, Faculty of Sciences, Fez, Morocco in 2014. His research interests include stability theory, robust control, Fuzzy systems and polynomial systems.

Hicham El Aiss received his Master’s degree in signals systems and informatics from the Faculty of Sciences at University Of Sidi Mohamed Ben Abdelah, Morocco, in 2013; he is currently a Ph.D. student in the same Faculty. His current reserch interests include delay systems, stability theory, robust control and Fuzzy systems.

Ahmed El Hajjaji received his Ph.D. degree 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 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.

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Chaibi, R., El Aiss, H., El Hajjaji, A. et al. Stability Analysis and Robust H∞ Controller Synthesis with Derivatives of Membership Functions for T-S Fuzzy Systems with Time-varying Delay: Input-output Stability Approach. Int. J. Control Autom. Syst. 18, 1872–1884 (2020). https://doi.org/10.1007/s12555-018-0802-6

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