H∞ controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities

This work presents an H_∞ controller design method for fuzzy dynamic systems based on techniques of piecewise smooth Lyapunov functions and bilinear matrix inequalities. It is shown that a piecewise continuous Lyapunov function can be used to establish the global stability with H_∞ performance of the resulting closed-loop fuzzy control systems and the control laws can be obtained by solving a set of bilinear matrix inequalities (BMIs). Two examples are given to illustrate the application of the proposed methods.