Robust Control Of The Uncertain Linear System

The stability and the performance are concerned most in the control systems. It is well known that the uncertainty, which is inevitable in practical systems, can destroy the systems' stability and performance. In order to maintain the system's stability and performance, the robust control attempts to describe the object's uncertainty and synthesize its controller within the perturbation scope permitted by the uncertainty. Therefore, in recent years, the robust control theory has been widely concerned and a lot of excellent results have been got in control field. Given this, the research of robust control theory has both important theoretical and pretty practical project significance. The objects studied in this article are the linear uncertainty systems.The problems in the robust control theory of the uncertain linear systems include both the robust stability analysis and the design of robust controller. As to the design of the robust controller, it refers to decide what kind of control structure and design method to use, so as to guarantee the system's more stronger robustness and deal with the influence of the system's uncertainty and disturbance. At present, the robust control research technique is generally divided into two kinds: One is the uncertain system analysis and design based on the system's robustness, especially the system's stability. The other is the control theory, which is designed according to the optimization of some kinds of performance index, such as H_∞control theory and guaranteed cost control theory.This article mainly deals with the guaranteed cost control for uncertain linear systems with closed-loop pole constrains. The condition of the existence of the feedback controller and its design method are proposed based on the present popular LMI method. What's more, the conditions of the exponential stability and the robust exponential stability of the uncertain linear systems with multiple time-varying delays and the non-memory state feedback design technique are given based on the LMI method.The main conclusions in this paper are:(1) The guaranteed cost control for the uncertain linear systems with closed-loop pole constrains on a given disk is discussed. A state feedback controller, which makes the closed-loop systems to be stability for all admissible uncertainties and the closedloop performance index no more than some given upper bound, is designed. The necessary and sufficient condition of the existence of the state feedback controller is given by using LMI. Based on the solution of LMI, the design method of guaranteed cost controller is obtained.(2) On the previous conclusion, since the state vector is not observable, the article attempts to design the dynamic output feedback controller, which makes the closed-loop systems to be stability for all admissible uncertainties and the closedloop performance index no more than some given upper bound. The necessary and sufficient condition of the existence of the dynamic output feedback controller is given by using LMI. Based on the solution of LMI, the design method of guaranteed cost controller is obtained.(3) The conditions of the exponential stability and the robust exponential stability of the uncertain linear systems with multiple time-varying delays and the non-memory state feedback design technique are given based on the LMI method.