Stability of discrete-time switched linear system with polytopic perturbations

In this paper, the asymptotic stability for discrete-time switched linear system with polytopic perturbations is considered. First, a sufficient condition for asymptotic stability is derived. It is shown that the discrete-time switched linear system with polytopic perturbations can be asymptotically stable for arbitrary switching signals if above condition is satisfied. Then, another sufficient condition for asymptotic stability is concluded in a different way, this condition is gained based on the convex combination technique and the norm boundedness; of the polytopic perturbation matrices. To make our results less conservative, the third sufficient condition together with a switching law based on state feedback is obtained. This condition is expressed as matrix inequalities with respect to a set of non-negative scalars and a positive definite matrix. By state feedback, we mean that the switchings among subsystems depend on system states. Finally, an example is proposed to illustrate the effectiveness of our results.