H_∞ controller synthesis of uncertain piecewise continuous-time linear systems

An H_∞ controller synthesis method is presented for uncertain piecewise linear systems based on a piecewise smooth Lyapunov function. The basic idea of the proposed approach is to search for a piecewise controller and a piecewise continuous Lyapunov function simultaneously and constructively so that the global stability with H_∞ performance of the resulting closed-loop control systems can be established. It is shown that the control law and Lyapunov function can be obtained by solving a set of bilinear matrix inequalities (BMI). Two examples are given to illustrate the application of the proposed method.