On The Simultaneous Strong Stabilization Of Discrete Linear Time-varying Systems

In this paper, we study the simultaneous strong stabilization of discrete time-varying linear systems in an operator-theoretic framework.The main work of this paper consists of the following subjects:1. Strong stability of discrete time-varying linear systems.2. Parametrization of all stable stabilizable controllers of linear systems.3. Simultaneous strong stabilization of two discrete time-varying linear systems.4. Simultaneously strong stabilization problem of a family of discrete time-varying linear systems.In Chapter 1, we review the control theory of linear system from point of view of mathematics. More precisely, we introduce the development of stability theory and also introduce main achievements obtained by some mathematicians in the research fields of stability of time-varying linear systems in an operator-theoretic framework.In Chapter 2, we introduce the basic knowledge of mathematics and control theory, such as the basic knowledge of operator theory, the background of discrete time-varying linear systems and the tools for the stability of feedback systems.In Chapter 3, we present the main result of this paper. First of all, we give the necessary and sufficient condition of strong stability of discrete time-varying linear sys-tems. Furthermore, we introduce the parametrization of all stable stabilizable controllers of linear systems. Finally, given the condition of simultaneous strong stabilization of a family of linear systems.In Chapter 4, we give the conclusion of this paper.In a word, we mainly study strong stabilization of discrete time-varying linear systems in an operator-theoretic framework, and we make some attempts to improve the traditional method concerning this problem.