Stability and strong passivity of nonlinear descriptor systems

In this paper, Lyapunov stability and strong passivity are defined for nonlinear descriptor systems. A Lyapunov stability theorem which describes a sufficient condition for the systems to be globally asymptotically stable and of index one is derived. By the Lyapunov stability theorem, the connection between Lyapunov stability and strong passivity is established. Furthermore, strong passivity of feedback systems is discussed and two passivity theorems are given. Using the given passivity theorems, we propose a stability criterion for Lur´e type descriptor systems (LDS).