The Invariance Principle of Singular Nonlinear Systems and Its Applications

Singular systems have extensive applications in modeling and control of many practical systems. The complex nature of singular systems cause many difficulties in the analysis and synthesis problems of singular systems. Linear singular systems have been studied extensively, and many valuable results have been reported. Recently, Singular nonlinear systems have attracted more and more attention. We know, Lasalle invariance principle plays an important role in conventional nonlinear systems. In this paper, the concept of E-invariant set is presented firstly, Lasalle invariance principle of conventional systems is extended to singular Nonlinear systems by citing the notion of E-invariant set and the generalized Lyapunov method, and the invariance principle of singular nonlinear systems is obtained at the same time. The sufficient conditions about the stability of singular nonlinear systems are given. Furthermore, the practicability and flexibility of invariant principle of singular systems are shown by illustrative examples.