Stability Analysis And Stabilization For Bilinear Singular Systems And Singular Large-scale Systems

The stability problem is one of the fundamental problems in the theory of singular systems. More and more scholars have been attracted by singular system with the rapid development of technology science and the need of practical problems.The stability and stabilization problems of bilinear singular systems and singular large-scale systems are discussed in the paper.The main contents and results in this dissertation are as follows:First of all,the stability and stabilization problems of bilinear singular systems which are under the continuous and discrete conditions are studied. The stability of bilinear singular systems under the allowed conditions is investigated by Lyapunov method. The stability criterions of bilinear singular systems are given and a feedback law is designed using the corresponding Riccati equation to stabilize bilinear singular systems.Further more,the stability and stabilization of continuous singular large-scale systems and discrete singular large-scale systems are investigated by Lyapunov method. The internal connecting matrixes and nonlinear parts are bounded by matrix norm. The stable Criterions and stabilization methods are given.At last,based on the researches of discrete singular systems,which are added time-delay parts and uncertain parts,the stability and stabilization problems of time-delay uncertain discrete singular large-scale systems are investigated by using Lyapunov method.Under the condition that all of the isolated subsystems are allowed, appropriate Lyapunov functions are found.Then the sufficient condition of stability are given.