A Series Of Nonlinear Systems, Robust H_ ¡Þ Control And Adapt To The H_ ¡Þ Control

This paper is concerned with the problems of robust H_∞ and adaptive Hr, control for a class of mismatched nonlinear systems with parameter uncertainty, based on a Lyapunov approach. The system under consideration is composed of two cascaded subsystems. When robust problem is discussed, the uncertain parameters are from a known compact set and are allowed to enter the system nonlinearly. A nonlinear static-state feedback controller is designed such that the L2 -gain of the closed-loop system is below a prespecified value for all admissible uncertainties without solving H-J-I equations. Furthermore, the closed-loop system is shown to be robust input-to-state stable under some conditions. When adaptive H_∞ problem is discussed, the uncertain parameters are not needed to be from a known compact set. A adaptive time-varying controller is designed such that the L2 -gain of the closed-loop system is below a prespecified value for all admissible uncertainties under convex assumption.