Robust Control Of Linear System With Time-Delay And Interconnected Systems

This paper mainly discusses robust stabilization of linear uncertain system with time-delay, decentralized robust stabilization of uncertain interconnected systems with time-varying delays and guaranteed cost control of interconnected systems, which play an important role in the control theory. The main results of this paper include three parts: Firstly, Stabilization of linear uncertain system with time-varying delay is researched, and the uncertainty under consideration is time-varying and unstructured, which contain not only in state terms but also in control term. On a certain assumption, by using Lyapunov method, Riccati equation approach and some inequalities are developed to propose a memoryless stabilization controller which renders the system asymptotically. Then in the research of uncertain interconnected systems with time-varying delays, high structured uncertainty, matrix polytope structured uncertainty and norm bounded uncertainty are discussed on the basis of Lyapunov stability theorem. Combining with inequalities, the existence conditions of controllers are equal to the feasibility of a series of LMIs(Linear Matrix Inequality), and memoryless decentralized robust controllers are given. Moreover, the optimal decentralized robust stabilization is discussed and a set of protruding optimize models are obtained. Finally, high structured uncertainty, matrix polytope structured uncertainty and norm bounded uncertainty are discussed in decentralized robust guaranteed controlling of uncertain interconnected systems. The existence conditions of guaranteed cost controllers expressed as LMI are obtained, in addition, the design methods of decentralized robust guaranteed cost controllers and the optimal guaranteed cost controllers are proposed. We also obtain a set of protruding optimize models. The conclusions in this paper mainly express as LMIs, therefore Matlab can be used to get the solutions conveniently. Then we give relative numerical examples to demonstrate the feasibility and effectiveness of the results obtained.