Abstract: The uncertainties of the linear switched systems with polytopic perturbations are formed by a convex combination of several known constant matrixes. For such systems, based on the convex combination of certainties and the norm concept of polytopic perturbations matrix, the single-Lyapunov function technique and multiple-Lyapunov function technique are used to give the sufficient conditions for the asymptotic stability and the design of switching laws, respectively. All the results are expressed by linear matrix inequalities which are easy checked in practice. The simulation results show the effectiveness of the method.