Control Lyapunov functions for switched control systems

The concept of control Lyapunov functions for nonlinear control systems is generalized to switched control systems. The existence of a control Lyapunov function is shown to be sufficient for a switched control system to be globally asymptotically. stabilizable. For switched systems affine in control, the control law and switching law are explicitly constructed. Quadratic control Lyapunov functions are also studied.