Guaranteed Cost Control And Robust H∞ Filter Design Of Some Time-delay Systems

Because of the changing of running environment and ot her immeasurable distur-bances, it is impossible to obtain the exact mathematics model of practical systems. The difference usually can be described as the uncertainties. Moreover, time de-lays are frequently encountered in a variety of practical systems. Uncertainties and time delays are often sources of instability and poor performance in systems. The robust control theory for uncertain time-delay systems is mature, but there are few contributions to the problems of nonlinear systems with multiple time-varying de-lays. When the system takes on non-full states, which include fast and slow states, it is named as singular system. Singular systems widely appear in the study of some naturally occurring systems than regular ones. e.g. in electric power systems, biochemical process, nuclear reactor, airplane and rocket systems. Therefore, the discussion on robust control for uncertain singular systems with delays is key both in theory and in practice.The main conclusions in this paper are as follows:(1)Based on the Lyapunov stability theory, the problem of mixed memory and memoryless guaranteed cost controller design for nonlinear systems with multiple time-varying delays is considered. A sufficient condition for the existence of mixed guaranteed cost controller and the design of the corresponding controller are pro-posed by the method of linear matrix inequalitics(LMIs). what's more, the method of finding the minimum performance specification is given. At last, a numerical example demonstrates that the designed method is effective and less conservative.(2)The problem of non-fragile guaranteed cost controller design for a class of uncertain singular Lur'e systems with time-delay is discussed. The idea of non-fragile guaranteed cost controller is introduced to uncertain singular Lur'e systems with time-delay and sector restricted nonlinearities. Based on linear matrix inequal-ity(LMI) techniques, the non-fragile guaranteed cost controller is designed. For the additive perturbation, the sufficient conditions for the existence of non-fragile guar-anteed cost controller is addressed. Simultaneously, the corresponding controller and the minimum guaranteed cost specification are proposed. At last, a numerical example is illustrated to demonstrate the effectiveness of this method.(3)The problem of robust H∞filtering for uncertain systems with time-varying state delays and time-varying neutral delays is considered. The uncertainties are norm bounded. The purpose is to design a full filter such that the filtering error dynamic system is asymptotically stable and satisfies a prescribed H∞performance level, for all admissible uncertainties and time-varying delays. At last the effective-ness of the proposed design method is demonstrated by a numerical example.