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

Abstract

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.