Uncertain Time-delay Singular Systems Robust H_ ¡Þ Control

Time delays are often encountered in objective world and engineering practice. It has been shown that the existence of time-delays may severely reduce the performance of the system, in some cases, it may also lead to instability. Singular system is a kind of dynamic system of more general form and widely application background. Since 1970s, the research of singular system has made great progress, many results of normal systems are successively extended to singular systems. Singular systems contain many singular systems with time-delay which are the more general systems than normal systems. On the other hand, the robust control problem is an active field of the control theory, it has got a series of achieve-ments and successful applications in some engineering fields. The rich theory and advanced method of robust control problem provide effective tools for solving the endless problems of modern science and technology filed. In this paper, we mainly consider the problem of robust H∞control for uncertain singular systems by means of LMI method, the main contents are following:First, the problem of robust H∞control for a class of linear singular systems with a state constant delay is considered. By constructing an improved Lyapunov function, based on LMI, a sufficient condition that can make the system admissible and satisfy H∞performance index is obtained. In addition, as for the design of H∞controller, we use the state-feedback controller with a constant delay:u(t)=Kx(t)+Kdx(t-d)(d is a known constant), which fully considers the size of delay, has less conservatism than the memory-less controller:u(t)= Kx(t). At last, a numerical example is given to illustrate the efficiency of the proposed method.Next, the problem of robust H∞control for a class of linear singular systems with a state time-varying delay is researched. By constructing a new Lyapunov function, with the methods of the Jensen inequality and free-weighting matrix, we estimate the derivative of the Lyapunov function, and get a stability result with less conservatism. Based on this result, a sufficient condition that can make the system admissible and satisfy H∞performance index is presented. By solving the corresponding LMI, a state feedback controller that can make the closed loop system admissible and satisfy H∞performance index can be obtained. Then, the results are extended to the uncertain systems, and we get the design scheme of the robust H∞controller for the corresponding singular system. At last, a simulation example is given to show the feasibility of the control scheme.