Linear matrix inequality approach to local stability analysis of discrete-time Takagi–Sugeno fuzzy systems

• Published in: IET control theory & applications Vol. 7; no. 9; pp. 1309 - 1318
• Main Authors: Lee, Dong Hwan, Joo, Young Hoon, Tak, Myung Hwan
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 01.06.2013
• Subjects: convex optimisations; convex programming; discrete time systems; discrete‐timeTakagi‐Sugeno fuzzy systems; domain of attraction; fuzzy Lyapunov functions; fuzzy systems; iterative methods; iterative scheme; linear matrix inequalities; LMI constraints; local stability analysis; Lyapunov methods; mean value theorem; minimisation; polytopic type bounds; single‐parameter minimisation problems; stability; sufficient conditions; iterative methods; discrete time systems; convex programming; single-parameter minimisation problems; iterative scheme; mean value theorem; polytopic type bounds; sufficient conditions; fuzzy Lyapunov functions; linear matrix inequalities; discrete-timeTakagi-Sugeno fuzzy systems; local stability analysis; LMI constraints; convex optimisations; fuzzy systems; minimisation; DA; domain of attraction; stability; Lyapunov methods
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2013.0033

This study deals with the problem of local stability analysis and the computation of invariant subsets of the domain of attraction (DA) for discrete-time Takagi–Sugeno fuzzy systems. Based on the fuzzy Lyapunov functions, new sufficient conditions and an iterative scheme are proposed in order to prove the local stability and to estimate the DA. The mean value theorem and polytopic type bounds on the gradient of the membership functions are used to consider the relation between the membership functions at samples k and k + 1. Each step of the iterative procedure consists of linear matrix inequalities (LMIs) or single-parameter minimisation problems subject to LMI constraints, which are solvable via convex optimisations. Finally, examples compare the proposed conditions with existing tests.