Study On Robust Control For Uncertain Systems With Time Delays

Time delay is common phenomenon in practical control systems. The three main reasons of bringing time delay are the transmission of material and signal, the measurement of system signal and some property of apparatus. Time delay as a source of instability and poor performance often appears in many dynamic systems, therefore, it is important to study of robust control on time delay system with ucertainties.The dissertation are mainly on the study of the robust stability analysis and controller design on the uncertain systems with time delays. The organization of this dissertation is as follows:In chapter two, the problem of robust stability for uncertain linear systems with time-varying delay and nonlinear perturbations is investigated. By contructing some appropriate Lyapunov-Krasovskii functionals, a new and less conservertive delay-dependent stability criteria is presented, which is in terms of linear matrix inequalities which can be solved numerically using Matlab Control Toobox.In chapter three, the problem of non-fragile guaranteed cost control for a class of uncertain stochastic nonlinear time-delay systems is considered. A new memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square for all admissible parameter uncertainties, time delay and controller gain variations and the closed-loop cost function value is not more than a specified upper bound. The obtained sufficient condition for the existence of such controllers is presented based on the linear matrix inequalities approach.In chapter four, the robust stability analysis problem for uncertain T-S fuzzy system with time-varying delay is investigated. Based on the Lyapunov-Krasovskii functional approach, sufficient condition for the asymptotic stability of the system is obtained. The key point of this study is that the time-varying delay function maybe not continuously differentiable and its derivative maybe not smaller than one. Compared with the other results, the obtained results are less conservative.Last but not the least, the problem of stochastic robust stability of a class of stochastic Hopfield neural networks with time-varying delays and parameter uncertainties is investigated. Based on stochastic analysis approaches, some new stability criteria are presented in terms of linear matrix inequalities (LMIs) to guarantee the delayed neural network to be robustly stochastically asymptotically stable in the mean square for all admissible uncertainties. Numerical examples are given to illustrate the effectiveness and less conservativeness of the developed techniques.