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

Research of switched systems, singular systems, nonlinear systems and related theories are introduced. The research background is given briefly and the significance of research is indicated. Based on Lyapunov theory and im-plicit function theorem in this paper, in terms of LMIs technique, the stability problems, the robust stability and robust state feedback stabilization problems and the static output feedback stabilization problems are discussed for a class of nonlinear discrete-time singular switched systems.(1) In chapter2the stability problem for a class of nonlinear discrete-time singular switched systems is investigated. First, based on Lyapunov theory and implicit function theorem, linear matrix inequalities (LMIs) sufficient con-dition is developed which guarantees that the nonlinear discrete-time singular switched systems are regular, causal, have unique solution in neighborhood of the origin, and are uniformly asymptotically stable. Then, in order to fa-cilitate the design of the controller, based on this condition, by using some matrix inequalities, another linear matrix inequalities(LMIs) sufficient condi-tion for the system to be regular, causal, have unique solution in neighborhood of the origin and be uniformly asymptotically stable is obtained. A numerical simulation is given to show the validity of the proposed methods.(2) In chapter3the robust stability and robust stabilization for uncer-tain nonlinear discrete-time singular switched systems are discussed. From the stability condition, robust stable sufficient condition is obtained, and the con-dition of existence and the design method of robust state feedback controllers are given. A numerical example is provided to illustrate the effectiveness of the proposed methods.(3)In chapter4, the static output feedback stabilization problems for a class of nonlinear discrete-time singular switched systems is discussed. Based on the stability condition and singular value decomposition approach, the con-dition of existence and the design method of static output feedback controllers are given. A numerical example is provided to illustrate the effectiveness of the proposed method.In this paper, there are three innovations. The first innovation is that for a class of nonlinear discrete-time singular switched systems which the nonlin-ear function satisfied a quadratic constraint, by Lyapunov theory and implicit function theorem, a sufficient condition for the system to be regular, causal, have unique solution in neighborhood of the origin and be uniformly asymp-totically stable is obtained.The second innovation is by some equivalent transformation of linear ma-trix inequalities, another stability sufficient condition to facilitate the design of the controller is obtained.The last innovation is that by using the singular value decomposition approach, the design method of the static output feedback is obtained. 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 in this paper can be solved clearly.