External stability of switching control systems

This paper investigates external stability (defined by the normal L2 norm) of switching control systems. It proposes definitions of the maximum, minimum dwell time for switching systems and then derives an important relation between the number of switchings and the maximum, minimum dwell time. Applying this relation, it establishes criteria on external stability of switching control systems consisting of Hurwitz stable subsystems. Furthermore, a switching law is proposed, and is proven to be realizable. Given this proposed switching law and applying the previous derived relation, the switching control systems comprised of both Hurwitz stable and Hurwitz unstable subsystems are proved to be externally stable.