Necessary and sufficient condition for the existence of a common quadratic lyapunov function for switched linear interval systems

In this paper, a necessary and sufficient condition for the existence of a common quadratic Lyapunov function (CQLF) for continuous time n-th order switched linear interval systems (SLISs) under arbitrary switching is presented. SLISs have infinitely many subsystems that are within the specified interval. All the subsystems of SLISs can be represented as a polytope of vertices of the interval matrix. It will be shown that the existence of a CQLF for SLISs is equivalent to the existence of a CQLF for all the vertices of the systems.