Quadratic stability results for switched singular descriptor linear systems

This paper addresses the issue of quadratic stability for a class of switched singular descriptor linear systems. A system of this class is a switched system whose subsystems are all singular systems. The convex combination technique for the standard switched systems is extended to switched singular descriptor linear systems to derive a sufficient condition of quadratic stability. For a switched singular system with two subsystems, a necessary and sufficient condition of quadratic stability is obtained. A stabilizing switching law is also designed. Finally, an example is given to illustrate the validity of these new results.