Stability And Stabilization For A Class Of Nonlinear Discrete-Time Singular With Time-Delays Systems

Research of singular systems, time-delay systems, nonlinear system and related theories is introduced and then the current research of the stability and stabilization problems for a class of nonlinear discrete-time singular time-delay systems is given. The significance of research is indicated and research back-ground is given briefly. Based on on Lyapunov theory and implicit function theorem, the stability, state feedback stabilization and static output feedback stabilization problems for a class of nonlinear discrete-time singular systems with time-delay are discussed via linear matrix inequality(LMI) respectively.In chapter2. the stability problem for a class of nonlinear discrete-time singular systems with time-delay is investigated. First, based on Lyapunov theory and implicit function theorem, an LMI sufficient conditions is developed which guarantee that the nonlinear discrete-time singular time-delay systems are regular, causal, have unique solution in a neighborhood of the origin, and are uniformly asymptotically stable. And some corollaries are obtained to proved the conclusions of some reference. Then, in order to facilitate the design of the controller, based on this condition, by using some matrix inequalities, another sufficient condition for the system to be regular, causal, have unique solution in a neighborhood of the origin and be uniformly asymptotically stable is obtained. A example simulation is given to show the validity of the proposed methods.In chapter3, the state feedback and static output feedback stabilization is investigated. From the stability theorem just in last chapter2, the sufficient conditions of which can be used to design state feedback controller is obtained, and the design method of static output feedback controllers are given with the singular value decomposition approach. Numerical examples are provided to illustrate the effectiveness of the proposed methods.One innovation is that for a class of nonlinear discrete-time singular time-delay systems which the nonlinear function satisfied a quadratic constraint, by Lyapunov theory and implicit function theorem, an LMI sufficient condition for the system to be regular, causal, have unique solution in a neighborhood of the origin and be uniformly asymptotically stable is obtained.Other innovation is that by some transformation of matrix inequalities, another stability sufficient condition is obtained which can be design the con-troller easily. The last innovation is that by using the singular value decom-position approach, the design method of the static output feedback controller. In this paper, there are no constraints to the output and input matrices of the system, all the conditions obtained are LMIs and expressed by the original coefficient matrices of the system. And all conditions obtained in this paper can be solved directly.