Stabilization of nonlinear systems using vector Lyapunov functions

This paper deals with the stabilization problem of nonlinear systems using vector Lyapunov methods. The stabilization of general nonlinear systems is posed in terms of the existence of some vector Lyapunov function which together with comparison principles allows us to compute the stabilizing controller. The design procedure consists of giving a comparison system satisfying the desired stability requirements and proposing some vector Lyapunov function then, the stabilizing control law is computed from certain differential inequality. For nonlinear systems affine in the control input the computation of a closed-form expression for the control law is indeed guaranteed by the existence of some control Lyapunov function. Copyright (C) 1998 IFAC..