Advanced Stability Conditions for TS Fuzzy Systems via Minimum-Type Multiple Switching Lyapunov Function

Abstract

This article deals with the stability analysis of TS fuzzy models using the novel minimum-type multiple switching Lyapunov function. A method is presented to investigate the stability of the model which consists of three separate steps; mesh the space of the model using the Delaunay method, considering a quadratic function for each vertex of the mesh, proposing a set of conditions based on the declared quadratic functions. The proposed conditions can be categorized into two sets; local and discontinuity conditions. The local conditions exploit the local stability in each simplex of the mesh which have minimum-type multiple forms. The discontinuity conditions force the global Lyapunov function to decrement in the switching points (boundary of the neighbor simplexes). To validate the result of the proposed approach, comparative simulation examples are given to illustrate the performance of the design methodology as compared to those of previous approaches.