Abstract
In this paper, we propose the method of stability analysis of nonlinear fuzzy systems using Multi-max/min based Lyapunov functions. Multi-max/min based Lyapunov functions have the generalized form of piecewise Lyapunov fuctions. We show that our method provides more efficient conditions for the stability analysis of nonlinear systems than the existing method using two-term quadratic piecewise Lyapunov functions do. First, we discuss about the inequations derived from Multi-max/min based Lyapunov functions in general case. Secondly, we apply these topics to fuzzy systems and derive the stability conditions in the form of BMI (Bilinear Matrix Inequarity) by using S-procedure lemma and propose the approach which combines MATLAB LMI Control Toolbox and PSO to estimate the solutions of BMI, which is difficult to solve. Finaly, we analyze a numerical example to show that our method provides more relaxed stability results than existing piecewise Lyapunov functions method.
