Research Of Continuous Time-Delay Singular System With Input Saturation

The study of time-delay singular system becomes a hotspot in the field of control, and has attracted more and more researchers. Under some conditions, some problems can only be described by time-delay singular system, such as complex circuit network model, the economic dynamic input-output model, the problem of environmental pollution model and so on. Input saturation factor is a general non-linear phenomenon. Without considering the input saturation factor to design a controller, the stability of closed-loop system can not be ensured. However, the existing research results in the time-delay singular system with input saturation are rare.This paper studies the control problems of the time-delay singular system with input saturation by using Lyapunov approach and linear matrix inequalities theory. Both the stabilization conditions and the design methods of H-infinity controller, robust controller and H-infinity guaranteed cost controller are given.The main research of this paper as following:First of all, the problems of H-infinity control for both linear time-delay singular system and nonlinear time-delay singular system all subject to input saturation are studied separately. And the design methods of H-infinity controller are given.Secondly, for a class of time-delay singular system with uncertain parameters subject to input saturation functions, the problem of H-infinity guaranteed cost control is studied. The existence conditions and design methods of robust state feedback H-infinity controller are given by using the Lyapunov stability theory and the method of linear matrix inequalities. And an illustrative example is given to explain the effectiveness of the proposed method. Finally, for a class of uncertain multiple time-delays singular system with input saturation, the problem of designing H-infinity controller is studied. A sufficient condition of robust H-infinity stabilization which satisfies guaranteed cost index is given for the system by constructing the generalized Lyapunov function, connecting with Schur Complete Lemma and taking the linear matrix inequality approach. Then the corresponding method of designing state feedback H-infinity guaranteed cost controller is given.