Robust Control Of Uncertain Linear Systems With Time Delays

The analysis of the stability of uncertain dynamic control systems withdelays and the synthesis of controller for them are important both in theoryand practice, the involved methods for the problem are numerous. The depthof its theories developed far more surmounted than this concreted problemcategory to solve robustness of particular control systems. This paperchooses an aspect of the theories to research according to the author'scomprehension. From the angles of the engineering fulfillment, in this paperwe apply the important theories and methods such as Lyapunov method,quadratic stabilization of time-varying uncertain systems and the linearmatrix inequality and so on to study series of robust control problemssystematically. This paper emphasizes on two aspects: One is performance,studying more system performance indexes which are under the premise thatsystem is stable to show the higher research value; the other is synthesis,facing various control objects, the engineering initial problems become towe should obtain a set of systematical methods of synthesis for controller,secondly we should use the method flexibly and consummate it interiorly.Generalize the research results of this paper; it is based on the linearuncertain systems. Moreover, the nonlinear and jumping dynamic systemswith time-delays are considered, and then it is put forward the uniformprocessing frame. It is studied the synthesis problems which are focused onthe stability, H_∞performance index of the systems. From the research results, it is clearly showed that if the bound of the performance index is under adefinite value, the synthesis of controllers that mentioned above can convertinto the problems which are able to solve by linear matrix inequalities (LMI).The LMI approaches have the mature arithmetic; therefore the researchresults in this paper are feasible and useful.The work of this dissertation mainly addresses the issues for robustcontrol of linear uncertain systems with time-delays. In detail, the majorcontribution of this dissertation as follows:1. This paper deals with the problem of delay-dependent robustH_∞control for uncertain linear systems with time-varying delays bothin state and input. Based on an integral inequality, the sufficientcondition of the existence for the state feedback controller is presentedin terms of LMI, By means of Lyapunov-Krasovskii functionalapproach; it is proved that the new criterion does not require anyassumptions about the system matrices.2. This paper deals with the problem of finding the robust fuzzycontroller to achieve the robust stability with guaranteed cost for aclass of uncertain time-delay systems. Based on the Takagi-Sugenofuzzy model, the robust stability condition is derived to ensure therobust quadratic stability of the system by applying Lyapunovfunctional approach and the upper bound of considered cost is found.Moreover, a fuzzy controller is developed to stabilize the uncertainsystem and the guaranteed cost function is get.3. This paper presents relaxed stability conditions for discrete-time T-Sfuzzy control systems. In order to widen the applicability of the fuzzycontrol approach, fuzzy control systems with uncertain grades ofmembership are investigated. New relaxed stability conditions are derived. It is shown that there is much freedom for choosing thecontrol law in the stability conditions.