Stability and robust stabilization of nonlinear descriptor systems with uncertainties

In this paper, we consider the problems of stability and robust stabilization of nonlinear descriptor systems. 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 on nonlinear descriptor systems developed above, we also discuss the robust stabilization problem of an important class of nonlinear descriptor systems with uncertain perturbations, and propose a class of stabilizing state feedback controllers for this class of uncertain descriptor systems