Title: Delay dependent stability analysis of Takagi-Sugeno fuzzy time-delays system

Authors: Hadil Soltani; Rafika El Harabi; Saloua Bel Hadj Ali; Abdel Aitouche; Mohamed Naceur Abdelkrim

Addresses: MACS Laboratory, National Engineering School of Gabes, University of Gabes, Street Omar IBN Elkhatab Gabes, 6029, Tunisia ' MACS Laboratory, National Engineering School of Gabes, University of Gabes, Street Omar IBN Elkhatab Gabes, 6029, Tunisia ' Preparatory Institute for Engineering Studies, El Manar University, El Manar, Tunis, Tunisia ' CRIStAL UMR CNRS 9189, School of High Studies Engineer Lille, Lille, 59046, France ' MACS Laboratory, National Engineering School of Gabes, University of Gabes, Street Omar IBN Elkhatab Gabes, 6029, Tunisia

Abstract: Generally, nonlinearities and time-delays are inherent characters for the Takagi-Sugeno fuzzy system. There has been a lot of research works dealing with this type of systems. Most of these researches are based on measurable states but not all states are available in many physical systems. When such case happens, an observer is designed to estimate the system unavailable states. This work addresses the problem of stability analyses and stabilisation for the Takagi-Sugeno fuzzy system with time-delays. Motivated by recent concerns in stability issues, a stabilisation observer controller for Takagi-Sugeno fuzzy time-delay systems is re-evaluated in this paper. Based on the fuzzy weighting dependent Lyapunov-Krasovskii function approach, we provided, in terms of linear matrix inequalities, the sufficient conditions for the existence of a robust state feedback parallel distributed compensation controller that guarantees stability and finding the maximum delay bounds. The effectiveness and the applicability of the designed stabilisation controller are illustrated via the truck trailer systems.

Keywords: Takagi-Sugeno fuzzy system; time-delay system; stability; linear matrix inequalities; LMIs; parallel distributed compensation; PDC.

DOI: 10.1504/IJDSSS.2019.103383

International Journal of Digital Signals and Smart Systems, 2019 Vol.3 No.1/2/3, pp.150 - 172

Received: 13 Mar 2019
Accepted: 02 Apr 2019
Published online: 05 Nov 2019 *

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