Stabilization of a class of switched systems with unstabilizable switchin modes

This paper considers the stabilization of a class of switched control systems. Every switching mode is assumed to be not stabilizable. First, the linear case is considered. Assume the switching strategy and control are designable, a new stabilization technique is proposed, which stabilizes the unstabilizable sub-system by proper switching strategy and then stabilizes the stabilizable sub-system by using common quadratic Lyapunov function approach to the closed-loop sub-system. An easily verifiable sufficient condition is obtained. An illustrative example is provided to demonstrate the design procedure. Then using Lyapunov function with homogeneous derivative, similar design technique is used to stabilize switched nonlinear systems.