The Stability And Decentralized Stabilization Control For Generalized System

In the light of the recent work on generalized systems models, the dissertation provides a systematic study on the stability, decentralized stabilization control of parametric uncertainty and guaranteed cost control of generalized systems models. This paper addresses the problems of robust stable and robust stabilization for uncertain generalized systems with parameter uncertainties via linear matrix inequality (LMI) method. The parameter uncertainties are assumed to be time invariant, but value bounded. The purpose of the fundamental issues robust stabilization in this paper is to design state feedback controllers so that, for all admissible uncertainties, the closed-loop system is regular and stable causality. In terms of strict LMI, sufficient conditions for the solvability of above problems are presented, and the parameterizations of the desired state feedback controllers are also given.For a class of generalized systems with value bounded parameter uncertainty and a quadratic performance index, the problem of designing a guaranteed cost state feedback controller is designed. Based on the expression of uncertainty a sufficient condition for the existence of the guaranteed cost decentralized controller is derived by linear matrix inequality (LMI) approach and the Lyapunov function.A class of singular systems with symmetric interconnected and identical structure was investigated. The original singular symmetric composite systems were transformed to n lower-order modified subsystems via systems transformation. Then it was found that the characteristics such as stability, controllability, observability, the existence of a fixed mode, decentralized normalization, the solution of the Lyapunov equation and Riccati equation. This kind of singular systems can be determined by the corresponding properties of the n lower-order modified subsystems.