Practical Stability Analysis and Synthesis for Nonlinear Singular Systems

Abstract

Practical stability, being quite different from stability in the sense of Lyapunov, is a significant performance specification from an engineering point of view. In this chapter, practical stability of nonlinear singular systems is studied. The basic concepts and results on practical stability for standard state-space systems are generalized to singular systems. First, some sufficient conditions for nonlinear singular systems to be practically stable are derived by Lyapunov stability theory and comparison principle. Second, practical stability of nonlinear singular systems with disturbance inputs is studied by comparison principle. Third, practical stability in terms of two measurements is investigated for nonlinear singular systems with time delays and some sucient conditions are derived by using Lyapunov stability theory and comparison principle. Finally, the problem of practical stabilization of nonlinear singular systems is investigated. A controller design method is derived by introducing a new comparison principle.