Study On Robust Stabilization For A Class Of Linear Uncertain Time Delay Systems

Time delay is retard of signal transmission. Time delay can be found in various engineering systems such as chemical processes, biological systems, and economic systems. Stability is of primary importance for a system. Otherwise, as we all know, firstly, the existence of time-delay can produce a large number of effects to the stability of the system, because the existence of time-delay will change the proper equation of the system. As a result, time delay becomes the main factor to lead to instability of the system. Considering the control accuracy, we need to construct accurate mathematic model instead of simple disposal. Therefore, the study of time delay is indispensable and possesses great significance. At the same time, the development of modern mathematics, control theory and computer technology provide powerful tools for the study of uncertain time delay systems. However, in engineering practice, the model of control systems usually comprises uncertainty. Because it is difficult to get accurate mathematical model or the model is very complex, we have to simplify or approximate in analysis and design. In addition, more or less there exists external disturbance in the system, they can induce deterioration of system quality, even instability. It required that our dynamic system possess robust quality, which keeps intrinsic quality on condition that there exists uncertain factor. The uncertainty and external disturbance are regarded as perturbation in mathematics. Consequently, study on stability and control for time delay systems which include disturbance has important theoretical significance and practical value. Robust stability and robust stabilization for a class of linear uncertain time delay systems are studied in this paper,it is divided into five parts. 1.Firstly, the background and development of robust control for a class of linear uncertain time delay systems are proposed. 2.Theoretic basic needed such as lemma, definition, conception are given. 3.The problem of robust stabilization for linear uncertain time-delay systems with nonlinear perturbation is proposed. Based on Lyapunov stability theory, robust controller is given by analyzing the stability of closed-loop system. The sufficient condition for the existence of controller is deduced. Then, the condition is further equivalent to the solvability of certain linear matrix inequality (LMI). The controller designed guarantees the closed-loop system to be asymptotically stable and possess good maneuverability. 4.By analyzing the stability of closed-loop system, the criteria of robust stability and stabilization of delay-dependent for a class of uncertain time-varying delay systems with uncertainty is developed. 5.Delay-dependent robust controller design for uncertain input-delayed systems was proposed. Based on LMI feasible solution, the sufficient condition of robust stabilization and method of delay-dependent robust controller design were developed by constructing Lyapunov function. Finally, an example illustrated the validity and effectiveness of the proposed method.