A fuzzy Lyapunov function approach to stabilize uncertain nonlinear systems using improved random search method

Abstract

This paper addresses stabilization for Takagi-Sugeno (T-S) fuzzy systems with model uncertainties via a socalled fuzzy Lyapunov function, which is a multiple Lyapunov function. Based on the fuzzy Lyapunov function approach and a parallel distributed compensation (PDC) scheme, we provide stabilization conditions for closed-loop fuzzy systems with model uncertainties. Furthermore, we propose a compound search strategy composed of island random optimal algorithms concatenated with the Simplex method to identify the chaotic systems, and to solve the linear matrix inequality (LMI) problem. Finally, a numerical example of the Lorenz system is given to illustrate the utility of the proposed approach. Keywords-Fuzzy Lyapunov function, Linear matrix inequality, Model uncertainty, Random optimal algorithmsI.