Study On Guaranteed Cost Filter For Ucertain Systems With Time Delays

Uncertain time-delay system has long been one of the international poplar research fields. One of its main is that, actually, most of the control systems are inevitably influenced by varies kinds of uncertainties, which come from the system itself and external disturbance. At the same time, time delaying and arbitrariness are also widely found in many applicative systems, such as daily communication system, biological system, chemical industry system and electric power system. Thus time-delay often result in instability of the system, and also likely to damage the various performances of control system. So it becomes a very hot and difficult problem that how to suppress the performance degradation caused by time-delay and to reduce the conservatism of the control system. Therefore, it is of great theoretical and practical value to study the guaranteed cost filter of uncertain time-delay system. This paper mainly studies the stability of several uncertain time delay systems and methods to design the guaranteed cost filter. The organization of this dissertation is as follows:In chapter two, the robust L2-L∞guaranteed cost filter problem of a class of uncertain time-delay stochastic system is considered. By constructing proper Lyapunov-Krasovskii function, the resulting augmented system is robustly asymptotically stable and satisfies the proposed guaranteed cost performance. In terms of stability theory and LMI methods, a sufficient condition of existence of robust L2-L∞guaranteed cost filter is derived and a robust L2-L∞guaranteed cost filter is designed.In chapter three, the problem of robust H∞guaranteed cost control for a class of uncertain non-linear discrete stochastic systems is studied. Based on Lyapunov stability theory and linear matrix inequalities, a delay dependent stability criteria is proposed Furthermore, in terms of linear matrix inequalities, a robust H∞guaranteed cost controller is designed, which is a memory state feedback controller. It not only makes the closed-loop system to asymptotically stable in the mean square for all admissible parameter uncertainties and also guarantees a certain level of system performance.Last but not the least, the robust L2-L∞guaranteed cost filter problem of a class of uncertain time-delay systems with distributed delays is considered. The aim is to design a robust L2-L∞guaranteed cost filter and to obtain upper bound of the quadratic cost function.By constructing proper Lyapunov-krasovskii function, the resulting augmented system is robustly asymptotically stable and satisfies the proposed guaranteed cost performance. In terms of stability theory and LMI methods, a sufficient condition of existence of robust L2-L∞guaranteed cost filter is derived and a robust L2-L∞guaranteed cost filter is presented.