Robust Control Of Uncertain Time Delay Systems

Time delay systems exist widely in engineering practice,It has been indicated that the time delay can destroy the stability of system and degrade the control performance.Considering the control accuracy,we need to construct accurate mathematic model instead of simple disposal. However, the model of control systems usually comprises uncertainty.Because it is dificult 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.Consequently,study on stability and control for time delay systems which include uncertainty has important theoretical significance and practical value.H_∞control theory is a kind of powerful tool of analysing and designing uncertain system, which can solve control problems of control quality worsening due to the error of object model and model perturbation within acertain range.In this paper, the uncertain time-delay systems,based on Lyapunov stability theory,are extensively studied in the Linear Matrix Inequality(LMI) approach.The application of the LMI in the stability analysis for uncertain time-delay systems is discussed.and based on the performance,the robust H_∞controllers for a class of bounded uncertain linear time-delay systems with a time-varying state delay are designed.The development about uncertain time-delay systems and general situation about their research are discussed in the paper,and then the main methods and some tools,which will be used in heis dissertation,are introduced.Finally,some necessary preliminary results in this dissertation are given.The problem of H_∞robust control is investigated for a class of uncertain systems with time-varying delays in state and control input. If the results of the LMIs do exist,a type of static feedback controller is developed,which renders the closed-loop system asymptotically stable and satisfies a given disturbance attenuation H_∞performance.Finally an example is given to demonstrate the results.An observer-based robust decentralized control problem is investigated for a class of similar systems as that in chapter 3.It resolves such a problem that state feedback controller cannot be designed under the condition that system state cannot be measured or fully measured.Finally,a numerical example is presented to illustrate the results given in this paper. which shows that the method is very effective.An observer-based robust H_∞control problem is investigated for a class of uncertain linear systems with time-varying delays in state. By using the theory of Lyapunov method, a sufficient condition for asymptotically stabilizing the closed-loop systems is derived and the norm of the transfer function from the disturbance to the control output is reduced to a given level,if only if the results of LMIs exist.Both the controller and the observer are obtained.Finally,a numerical example is presented to illustrate the results given in this paper which shows that the method is very effective.The conclusion and perspectives are given in the end of the paper.