Robust H∞ control for a class of cascaded nonlinear systems

This paper is concerned with the problem of robust H_∞ control for a class of nonlinear systems with parameter uncertainty. The system under consideration is composed of two cascaded subsystems: a zero-input asymptotically stable nonlinear one, and a linearizable one which is controllable. The uncertain parameters are from a known compact set and are allowed to enter the system nonlinearly. Based on a Lyapunov approach, 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. Furthermore, the closed-loop system is shown to be robust input-to-state stable under some conditions