Passivity and Passivity based Controller Design of a Class of Switched Control Systems

Notions of passivity for a class of switched control systems (SCS) are developed in this article. We study the following problems: 1) When is an SCS passive? 2) Does passivity imply Lyapunov stability as in the classical passive systems? 3) How to use passivity as a tool to design controllers to stabilize an SCS? For Problem 1), we derive sufficient conditions for passivity. For problem 2), we show that passivity does imply Lyapunov stability when $u=0$, and the stability result obtained from positive semidefinite storage functions is new in switching systems. For the last problem, we first show that by designing the control law properly other than $u=0$, stronger stability results can be obtained for a passive SCS. Then, based on this, we solve the stabilization problem of an SCS by making it passive first and then designing the control law.