A Study On Robust Control For Uncertain Singular System With Time-delay

Uncertainties inevitably exist in all kinds of physical, industrial and engineering systems because of the simplification of model, change of running environment, aging of electrical elements and so on. Hence, it is difficult for the modern control theory, which is based on the exact mathematical model, to make control systems satisfy the desired performance. Also, time delay is frequently encountered in a variety of systems, such as nuclear reactors, chemical engineering systems, biological systems, and population dynamics model. It is often a source of instability and degradation of performance for the control systems. On the other hand, increasing attention has been focused on generalized systems due to the fact that they can better describe physical systems than state-space ones. Therefore, the analysis and synthesis of uncertain generalized time-delay systems are important both in theory and practice. There have been a lot of achievements on the stability and the basic theories, but robust control problem is less than it, many control problems also need continue research about them.In this paper, based on the Lyapunov stability theory, the linear matrix inequalities processing method is used to discuss robust preserving performance control,H∞control problems of uncertain singular time-delay systems, etc. The main contents of this thesis are stated as follows:(1) The designation idea of resilient controller is introduced to a class of uncertain singular system with time-delay. Based on linear matrix inequality (LMI) techniques, the problem of guaranteed cost control is addressed, where the uncertainties exist both in the systematic matrix and in the controller gain.(2) The robust H∞problem based on state-feedback control for uncertain singular system with time-varying delay is studied. By Lyapunov functional method, the robust stability and the sufficient condition of H∞norm bound for such system are presented. By LMI technique with equation constraints, the sufficient condition of the existence of state feedback controllers is provided in terms of a strict LMI feasibility. A parameterized representation of controller is characterized in terms of the feasible solutions to the strict LMI. The asymptotically stable condition of the designed robust controllers based on LMI is loose and has no equation constrains, which are usually included in the stability of singular system with time-delay.(3) The problem of H∞control for a class of uncertain singular system with time -varying delay is investigated. By means of Lyapunov functional method and LMI technique, a delay-dependent sufficient condition is presented to guarantee that the closed-loop system is regular and stable, and satisfies a prescribed H∞norm-bounded constraint. In terms of solutions of LMI, the H∞control law of singular system is presented. Moreover, compared with the existed results there is no need of model transformations in the proposed method.(4) This paper focuses on the robust H∞problem based on the static output feed- back control for uncertain singular system with time-varying delay. By Lyapunov functional method, a delay-dependent robust stability and sufficient condition of H∞norm bound for such system are presented. The sufficient condition of the existence of output feedback controllers is provided in terms of a strict LMI feasibility. A parameterized representation of controller is characterized in terms of the feasible solutions to the strict LMI. Compared with the old conditions, the delay-dependent stable condition of the designed robust controllers based on LMI has no equation constrains.