Analysis And Design Of Robust Performance For Uncertain Time-delay Systems

The problem of robust control for uncertain time-delay systems is discussed in this dissertation. To begin with, a general situation of robust control and the H∞theory of time-delay systems are summarized. After that, according to several different uncertain systems with time-delay, the conditions for robust asymptotically stable and the robust state feedback controller design method are studied. It is as follows.In the first place,Considering the properties of uncertainty and time-varying delay, the robust guaranteed cost control problem for a class of uncertain linear systems is discussed. A sufficient condition of robust asymptotically stable is derived and performance is obtained via the linear matrix inequality approach. Thereby, the robust memoryless state-feedback controllers are given by proved and a supreme boundary of performance index is presented. Finally, a numerical example is presented to illustrate the efficiency of the obtained result. In addition,Based on the Lyapunov functional and linear matrix inequality methods, the robust control of time-delay systems with uncertainty and nonlinear perturbation is decentralized. Some state-feedback controllers are designed which guaranteed that the systems are robust asymptotically stable. All the results are given in the form of linear matrix inequalities so that they are easy to be resolved.At last,The problem of non-fragile H∞control is discussed for a class of complex multiple time-delay systems based on a method of linear matrix inequality (LMI).Two robust controllers are presented under additive and multiplicative perturbations of controller gain. Several sufficient conditions for the solvability of the non-fragile H∞control problem are given in terms of LMIs. Under action of the given controllers, the systems are asymptotically stable and satisfy H∞performance. Finally, a numerical example is provided to demonstrate the validity of the proposed design approach.