Robust feedback design of a class of nonlinear cascaded systems with structural uncertainty

Abstract

This paper is concerned with the robust stabilization and robust L 2 disturbance attenuation of a class of cascaded nonlinear systems with structural uncertainties. The design tools are construction of a Lyapunov function for robust stabilization and a storage function for robust L 2 gain performance. It is shown that, if for each subsystem there exist Lyapunov functions satisfying Hamilton-Jacobi inequalities related with nominal subsystems, then a robust stabilizing controller can be constructed such that the sum of the functions becomes a Lyapunov function for the cascaded system with uncertainties. This concept, is extended do the construction of the storage function and the controller for the robust L 2 disturbance attenuation problem by introducing an appropriate weight into the sum of the subsystem's Lyapunov functions.