Lyapunov stability theory and robust control of uncertain descriptor systems

Abstract

In this paper we consider the problem of stability and robustness of uncertain nonlinear descriptor systems. The Lyapunov stability theory for conventional systems is extended in a natural way to nonlinear descriptor systems, and some stability theorems for descriptor systems are given. By making use of the stability results developed in this paper, we also discuss the robust control problem of an important class of nonlinear descriptor systems with uncertainties, and propose a class of stabilizing state feedback controllers for this class of uncertain descriptor systems. Finally, a numerical example is given to demonstrate the utilization of our approach.