Robust Stability And Robust H_∞ Control Problem For Nonlinear Singular System With Uncertainty

Recently, there has been a growing interesting in singular system for their extensive applications in control theory, circuits, economic, mechanical systems and other areas. Many conclusions in nonsingular system have been successively extended to singular systems. Sine nonlinear singular systems with uncertainties is more suitable to describe objective systems, therefore, it is necessary to study the nonlinear singular systems with uncertainties. This paper analyzes the recent research in robust control theory of the nonlinear singular systems with uncertainty, and study the problem of robust stability and robust H∞control in nonlinear singular systems with uncertainties. The main results in this paper are the following:This paper introduce the background, theory and the development profiles of singular systems in the first part. Next the stabilization problem of nonlinear time-varying singular system is investigated. The sufficient condition with impulse and stability of nonlinear time-varying singular system is proposed. Under the suitable conditions, fast subsystem changes is determined by slow subsystem and asymptotic stability criteria of nonlinear time-varying singular systems is proposed by utilizing Riccati equation. Next the problem of robust stability nonlinear singular systems with parametric uncertainties is studied. In this part, we discuss robust stability and the state feedback controller is designed for the robust stability of the closed-loop system by using Lyapunov theory and linear matrix inequalities. Under the right conditions, we obtain the condition which base on the robust state feedback control law. An example shows the feasibility and effectiveness of the designed method. Finally the problem of the robust H∞control for a class of nonlinear singular system with uncertainties is discussed .By using linear matrix inequalities (LMI), this paper gives the method of how to design a state feedback robust H∞controller, get a sufficient condition which closed-loop singular systems can be allowed and guarantee the transfered function H∞norm-bounded. At last, feasibility and effectiveness of the designed method have been verified by the programs.