Part Of The Decomposition Of Linear Discrete System Stability

Stability is an important structure characteristic for control systems. It is a necessary condition of normal work for the systems. The moving stability analysis for the control systems is an important research subject of control theory field. Recently, with the development of computer science, the stability for discrete-time large-scale systems is more and more regarded. In this paper, The stability for discrete-time large-scale systems is mainly considered. A partial decomposition for linear discrete large-scale systems in stability is proposed. And it is applied to stability analysis for the time-invariant and time-varying discrete large-scale systems. The organization of this paper is as follows.In chapter 1, a concise brief is done of stability for large-scale systems. And a summarization is made of research status and development trend for linear discrete large-scale systems. Lyapunov basic Theorems of stability for discrete systems are reviewed. The scalar Lyapunov function approach and vector Lyapunov function approach of stability for large-scale systems are analyzed. And it is pointed out that the restriction of these approaches are only suited for large-scale systems with week coupling among subsystems.In order to overcome the restriction of classical approaches of stability for linear time-invariant discrete large-scale systems, we study the stability for large-scale systems with unidirectional strong coupling among subsystems in Chapter 2. A partial decomposing approach is proposed, witch is suited for the stability for the discrete large-scale systems. By using the approach, a high-order linear discrete large-scale system can be decomposed into some low-order decoupling subsystems with unidirection. Then a higher order Lyapunov matrix equation can be transformed into some lower order matrix equations with unidirection coupling by using scalar Lyapunov function approach. The sufficient conditions of stability are obtained by matrix inequalities.In Chapter 3, we study the stability for linear time-varying discrete large-scale systems with unidirectional strong coupling among subsystems. The partial decomposingapproach is applied to the stability analysis for the linear time-varying discrete large-scale systems. By using the approach, a high-order linear time-varying discrete large-scale system is decomposed into some low-order decoupling subsystems with unidirection. By using scalar Lyapunov function approach, sufficient conditions of stability are obtained.The conclusion of the paper is done in Chapter 4, and the prospect of application range and development of the partial decomposing approach is presented...