Title: Further improvements on robust stability analysis for Takagi-Sugeno fuzzy systems with time-varying delay

Authors: Said Idrissi; Youssef El Fezazi; Nabil El Fezazi; El Houssaine Tissir

Addresses: LPFAS, Department of Physics, Polydisciplinary Faculty of Safi, Cadi Ayyad University, B.P. 4162, Sidi Bouzid, Safi, Morocco ' LISAC, Department of Physics, Faculty of Sciences Dhar El Mahraz, University of Sidi Mohammed Ben Abdellah, B.P. 1796, Fes-Atlas, Morocco ' LISAC, Department of Physics, Faculty of Sciences Dhar El Mahraz, University of Sidi Mohammed Ben Abdellah, B.P. 1796, Fes-Atlas, Morocco ' LISAC, Department of Physics, Faculty of Sciences Dhar El Mahraz, University of Sidi Mohammed Ben Abdellah, B.P. 1796, Fes-Atlas, Morocco

Abstract: This paper deals with the problem of robust stability analysis for uncertain Takagi-Sugeno (T-S) fuzzy systems with time varying delays. The approach is based on constructing an appropriate Lyapunov-Krasovskii functional (LKF) combined with state vector augmentation by using the delay-partitioning idea. By dividing uniformly the delay interval into N segments, with N as a positive integer, the LKF is chosen with different weighted matrices corresponding to different segments. The parametric uncertainties are assumed to be norm bounded. On this basis, new sufficient conditions ensuring the robust stability are expressed in terms of linear matrix inequalities (LMIs). Furthermore, the Finsler's lemma and the Seuret-Wirtinger's based integral inequality approach have been employed to derive less conservative results. Finally, numerical examples are provided to illustrate the effectiveness and the merit of the obtained results, compared with some previous works in the literature.

Keywords: Takagi-Sugeno fuzzy systems; delay partitioning approach; stability; Lyapunov-Krasovskii functional; LKF; time varying delays.

DOI: 10.1504/IJAAC.2023.133976

International Journal of Automation and Control, 2023 Vol.17 No.5, pp.487 - 505

Received: 03 Aug 2022
Accepted: 29 Nov 2022
Published online: 09 Oct 2023 *

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