Robust Stabilizations Of Uncertainty System And Neutral Nonlinear Large Scale Control Systems With Multi-group Multi-delay

By using Lyapunov stability theory, this note deals with the robust control of uncertain systems with time-varying delays and interval neutral nonlinear systems with multi-group multi-delay. Based on the model of state space, the problem of robust stabilization for time-delay systems with time-varying norm-bounded structure uncertainties and interval neutral nonlinear systems with multi-group multi-delay is considered. Furthermore, the sufficient conditions are derived for the systems discussed in this paper. As far as the delays is concerned, there are single delay, multi-delay, time-invariant delays and also time-varying delays in the systems studied in this paper. And for the uncertainties, some uncertainties concluded in this paper satisfy the so called " matching condition ", but others fail to satisfy the " matching condition ". In addition, some interval coefficient systems are also considered in this note.The contents of this dissertation are divided into five parts.Part one studies the robust stability for a class of system with time-varying delays, some stability criteria are devised by taking the relationship between the terms in Newton-Leibniz formula into account and using the linear matrix inequality (LMI). Then a class of systems with time-varying delays and time-varying norm-bounded structure uncertainties is considered. Under the assumption that the uncertain parts are norm-bounded, stability criteria are also obtained.Part two considers the problem of quadratic stabilization of continuous time system. The uncertainties in the system are assumed to be norm-bounded but they fail to satisfy the so called " matching condition ". Through introducing the concept of quadratic stabilization, this part gives a method of stabilizing a class of uncertain system by using state-feedback control law. This kind of state-feedback control lawcan be obtained by solving a certain algebraic matrix equation. The result has no conservative. This can be verified by a theorem in this paper.In part three, the robust stabilization of neutral systems with multiple time-varying delays and norm-bounded uncertainties are considered. By using linear matrix inequality(LMI) and taking a kind of peculiar Lyapunov-Krasovskii function into account, the sufficient conditions for the given systems are obtained.In part four, under the assumption that the nonlinear parts are norm-bounded, the robust stabilization of interval neutral type nonlinear time-invariant system with multi-group multi-delay is considered by using the equivalence method of control system with delays and without delays. The large scale systems can be divided into several isolated sub-systems and the nonlinear parts of the system are treated as the perturbation of the isolated systems. At the same time, the estimate formulae of interval length limitation and time delay limitation are given. Finally, the sufficient conditions of robust stability is obtained. We also give a example to demonstrate the effectiveness of the method proposed in this paper.At the last part of this paper, by using the same method as part four, the robust stabilization of interval neutral type nonlinear time-varying system with multi-group multi-delay is considered. The same sufficient conditions of robust stability are obtained.