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A H∞ controller synthesis method is presented for uncertai piece ise linear systems based o a piece ise smooth Lyapunov function. The basic idea of the proposed approach is to search for a piece ise controller and a piece ise continuous Lyapunov function simultaneously and constructively so that the global stability ith H∞ performance of the resulting closed-loop control systems ca be established. It is sho n that the control la and Lyapunov functio ca be obtained by solving a set of bilinear matrix inequalities (BMI). T o examples are give to illustrate the application of the proposed method.