An algorithm to compute invariant sets for third-order switched systems

We study invariant sets for switched systems. We focus on a class of third-order switched systems. In this class of switched systems we solve the problem of finding an invariant set for a switching law. For each switched system we provide the invariant set and the switching law, in addition, the invariant set is a polyhedral cone and the switching law is switching on the boundary. To accomplish this we reduce the problem to a simplified system. We provide a procedure calculating the invariant set. The method is based on calculating an invariant set for a simplified system and then transformating the invariant set to the original system. We illustrate this method with an example.