Lyapunov Stability and Strong Passivity Analysis for Nonlinear Descriptor Systems

In this paper, Lyapunov stability and strong passivity are defined for nonlinear descriptor systems. The new concepts facilitate the formulation of the relationship between the stability and passivity of 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, strongly absolute stability of Lur´e type descriptor systems is discussed. The obtained strongly absolute stability criterion is shown to be more general and less conservative than the existing methods. Finally, two examples are used to illustrate the advantages and effectiveness of the obtained methods.