Robust Control Of Uncertain Continuous Time-Delay Singular Systems

The singular system is a kind of dynamical systems of more general and extensive applied background. It has been developed sufficiently from 1970s and widely applied in power systems, economic systems, network systems and so on. Time-delay destroys the stability of system and degrades the control performance. So it is of a great importance in theoretical and practical application to study the robust control for the uncertainty continuous time-delay singular systems.This thesis studies the robust control problems for some uncertain continuous time-delay singular systems. The detail is clarified as follows: First of all, for a class of uncertain continuous time-delay systems singular, the problem of robust H∞control is investigated. Based on Lyapunov stability theorem, a state feedback H∞controller is designed by selecting an approximate Lyapunov function and using the inequality of Riccati.Secondly, by using linear matrix inequalities approach, the problem of quadratic stabilization for the uncertain continuous time-delay singular systems is studied and a sufficient condition of quadratic stabilization is given.Thirdly, the problems of H∞control and H∞guaranteed cost control for the uncertain continuous multiply time-delay singular systems are studied. Both state and input of the systems are with multiply time-delay, meanwhile output systems are with multiply time-delay. It is supposed that the time-varying uncertain parameters are norm-bounded, but the matched conditions are not required to satisfy. The designing methods of H∞controller and H∞guaranteed cost controller are obtained by using linear matrix inequalities approach. Then a numerical example is given to demonstrate the effectiveness of the proposed method. Finally, a conclusion of the thesis is given. At the same time, some perspectives for our future work are presented.