A Fuzzy Lyapunov Function Approach to Stabilize Uncertain Nonlinear Systems Using Improved Random Search Method

This paper addresses stability analysis and stabilization for Takagi-Sugeno (T-S) fuzzy systems with model uncertainties via a so-called fuzzy Lyapunov function, which is a multiple Lyapunov function. The advantage of the fuzzy Lyapunov function is that the controller design is not restricted by a common positive definite matrix (i.e., the common P) to form the quadratic 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.