State Feedback H-infinity Control For Continuous Or Discrete Delayed Singular Systems

The H-infinity control problems of the state feedback are studied respectively for a class of linear (or nonlinear) continuous (or discrete) singular systems with state and input delays in the paper,by means of LMI techniques and Lyapunov stability theory.In the first part, the H∞control problems for linear singular systems with time-delays are studied. Firstly, a sufficient condition is given for the system to be allowed and satisfied the H-infinity norm constraint. Secondly, a memory-less state feedback control law is designed which ensures the closed-loop systems have H-infinity property. So the stability of the system is obtained in terms of the corresponding controllers designed by the solution of the linear matrix inequalities which have been obtained in the paper. Lastly, a numerical example is given to illustrate the probability of the proposed method.In the second part, the H∞control problems are studied for a class of nonlinear singular systems with time-delays, of which the state equation can be divided into linear and nonlinear part. In some conditions, the nonlinear part can be transformed into linear questions by means of inequality. Further, the static feedback H∞controller is designed in terms of the Lypunov methods, so the sufficient conditions are obtained for the closed-loop system of the delayed nonlinear singular systems to be stable.In the third part, the problems of H∞control are studied for discrete linear and nonlinear singular systems with state and input delays. The static feedback controllers are designed and some conclusions are obtained for the delayed discrete singular systems to be allowed and satisfied the H-infinity norm constraint, which is easy realized on computer.Finally, some extensions about the H∞control problems of the singular systems are pointed out in the paper.