Vector control Lyapunov functions as a tool for decentralized and distributed control

This paper presents a novel tool based on vector control Lyapunov functions for complex nonlinear control systems. It is shown that the existence of a vector control Lyapunov function is a necessary and sufficient condition for the existence of a smooth globally stabilizing feedback. This main result is then applied to the problem of designing globally stabilizing feedback laws for nonlinear systems. Practically checkable sufficient conditions are proposed to guarantee the existence of a smooth globally stabilizing feedback law.