Stability Analysis And Stabilization For Nonlinear Singular Systems

With the incessant expansion of the fields of system theory and the increasing maturity and popularity of computer science, generalized control systems have been developed quickly. Since nonlinear singular systems are more suitable to describe objective systems, it is special necessary to research them. This thesis is outspreaded by nonlinear singular systems. The main contents and results in dissertation are as follows:(1) The background, the development of the theory and resent research achievements of singular systems have been introduced respectively.(2) The problems of stability for linear singular systems and nonlinear singular systems with time-varying have been studied. A sufficient condition is derived, in which linear singular system is supposed to be impulse-free and stable. Due to fact that the slow sub-systems can be determined by the fast sub-systems with appropriate conditions, we can get some concise criteria of stability for nonlinear singular systems has been gotten with time-varying by using Riccati equation.(3) The problems of stability for the nonlinear discrete singular systems have been studied. The method of singular Lyapunov function is employed to study the stability of nonlinear discrete singular systems. And the criteria of stability and the criteria of no stability have been given about it.(4) The problems of asymptotic stability and instability for the linear discrete singular large-scale systems and nonlinear discrete singular large-scale systems have been investigated. Under the condition that all isolated sub-systems are regular and causal, the concise criteria may be given to determine whether or not the discrete singular large-scale system be asymptotically stable or unstable by the method, of Lyapunov. At the same time the criteria of stability for nonlinear discrete singular large-scale systems are given.(5) The problem of stability and stabilization problem for linear discrete singular large-scale systems and nonlinear discrete singular large-scale systems with time-delay have been respectively investigated by using Lyapunov method. Under the condition that all isolated sub-systems are regular and causal, the concise criteria of linear discrete singular large-scale systems have been gotten by the Lyapunov method and it is to extend to the nonlinear discrete singular large-scale systems. So the criteria of stability can be gained.(6) The conclusion is given. And the perspective on the furthermore study is also proposed.Some numerical examples are given correspondingly to illustrate the effectiveness of the conclusions.