Stabilization And Stabilization With Internal Loop For Time-varying Linear Systems In The Framework Of Nest Algebra

In this paper, we use the operator theory to study the stabilziation problem of time-varying linear systems in the framework of nest algebra.In Chapter2, we simply introduce some preliminaries about the control theory of standard feedback systems in the framework of nest algebra and several basic problems on the stabilization of the standard feedback system.In Chapter3, the stabilization problem of the linear systems without given doubly coprime factorization is considered. We give a necessary and sufficient condition on the stabilization of the plant without known doubly coprime factorization. Then, we consider the simultaneous stabilization and robust stabilization problems. Movitated by the Youla parametrization, we give a characterization of the plant that can be simultaneously stabilized together with the given plant.In Chapter4, we study some control problems of the system with internal loop. This new model of system is firstly considered in the framework of nest algebra. In the previous paper, the controller with internal loop is assumed to be stable and satisfy two extra condtions. And only two special classes of controllers with internal loop called cannonical controllers and dual canonical controllers are widely investigated. Here, we consider the more general controllers with internal loop and originally give a parametrization of all stabilizing controllers with inter-nal loop. It is found that the parametrization of the canonical controller and dual canonical controller obtained before can be ragarded as a special case of the one obtained here. By using this parametrization, we consider the strong stabilization, simultaneous stabilization, robust sta-bilization and sensitivity minimization prolems for systems with internal loop. It is proved that any stabilizable plant can be strongly stabilized by controllers with internal loop. This means that the strong stabilization can be completely solved in the system with internal loop. While, in the framework of nest algebra, the strong stabilization problem in the standard feedback system is still an open problem. Thus, an advantage of the controller with internal loop is addressed in the framework of nest algebra. We give a necessary and sufficient condition on the simultaneous stabilization with internal loop for two plants. This result also implies an characterization of all simultandously stabilizing controllers with internal loop. It is shown that the simultaneous stabilization problem can be regarded as a subclasee of the problems of simultaneous stabiliza-tion with internal loop. In the end, we show the application and advantage of controller with internal loop on the study of sensitivity minimization problem.