H∞ control for asymptotically stable nonlinear systems

This paper deals with the problem of H_∞ control for a class of nonlinear systems. The system under consideration is assumed to be globally asymptotically stable with a known Lyapunov function. Based on this Lyapunov function and using the notion of dissipativeness, a state feedback controller is designed which renders the closed-loop system globally asymptotically stable with a prescribed bound on the L₂-gain from the disturbance input to the controlled output. The proposed controller design method is based on the explicit construction of a Lyapunov function for the closed-loop system, which represents a significant advantage over existing methods