Design Of H_∞Controller With Lower Conservativeness For Uncertain Linear Time-delay Systems

The time-delay phenomena often appear in practical systems such ascommunication systems, chemical processes, nuclear reactors, power systems andeconomy systems. Time-delay not only affects the stability of the system, but alsoaffects the dynamic performance of the system. The analyzed results of time-delaysystems are usually sufficient conditions, so a main motivation in studying time-delay systems is to reduce the conservativeness of the results. In this thesis, somenew delay dependent criteria for two classes of time delay systems are derived, statefeedback controller are then designed. When these conditions are used in theanalysis and controller design of polytopic uncertain systems, some lessconservative results are obtained. This thesis’s works include the following aspects.（1） For a class of time-delay systems with time-varying state delay, a class ofH_∞performance criterion in which the system matrices and the Lyapunov matricesare decoupled is derived by using the “Small Scalar Method”.（2） Based on the proposed H_∞performance criterion, a state feedback H_∞controller is designed for a class of time-delay systems with time-varying statedelay. The problem of the controller design is converted into the solution to aconvex optimization problem.（3） For a class of time-delay systems with interval time-delay rate, the H_∞performance and L₂-L_∞performance of the system are analyzed based on optimallydividing the delay interval. A class of criterion in which the system matrices and theLyapunov matrices are decoupled is derived based on the proposed criteria by usingthe “Small Scalar Method”.（4） An H_∞state feedback controller and an L₂-L_∞feedback controller aredesigned to improve the performance of a class of time-delay systems with intervaltime-delay rate based on the proposed criterion. The problems of the controllersdesign are both converted into the corresponding convex optimization problems.