Robust Control Theory And Applications Of Delay System

Robust control theory is the study of how to design the controller to ensure the resultantclosed-loop systems with uncertainties stable and satisfying a certain dynamic performance.Robust control problem is the the inevitable trend for development of modern control theoryand the only way leading to practical applications. Due to the feasibility in method andrationality in engineering，it has received extensive attention，Robust control are playing anincreasingly important role in the actual engineering controls. At present，robust control is stilla hot research field in control theory.In a variety of engineering，chemical and physical systems，Uncertainties inevitably existbecause of the simplification of model，change of running environment，aging of electricalelements and so on．Hence，it is difficult for the modern control theory，which is based on theexact mathematical model，to make control systems satisfy the desired performance，Also，time delay is commonly encountered in a variety of systems，such as power systems，unclearreactors，biological systems，chemical systems and so on．It is often an important source ofinstability and degradation of performance in those systems．Because of the widely used forthe background of time-delay systems，more and more scholars are concerned about it. So，thestudy of robust control for systems with time-delay (uncertain systems with time-delay) has agreat value both in theoretical significance and application value.In this paper，based on the Lyapunov stability theory，using the linear matrix inequalitymethod and delay decomposition approach，a series of problems of the time-delay systems isinvestigated， including robust stability analysis and the design of robust preservingperformance controller，etc. The main contents of this thesis are stated as follows:1. The problem of delay-dependent asymptotic stability for a class of uncertain linearsystems with time-delay is considered. A Lyapunov-Krasovskii functional is designed bysplitting the whole time-delay interval into N subintervals and defining different energyfunctions in every subinterval. A delay-dependent stability criterion is derived in terms ofLMI to ensure that the nominal system is stable.2. The problem of absolute stability of a class of time-delay Lurie systems is considered.By means of Lyapunov function and linear matrix inequalities (LMIs) technique， ALyapunov-Krasovskii functional is designed by splitting the whole time-delay interval into N subintervals and defining different energy functions in every subinterval a sufficient conditionfor the given systems with delay-dependent robust absolute stability is presented in term of acertain linear matrix inequality.3. The problem of nonlinear guaranteed cost control for a class of uncertain system withtime-delay is considered. Compared with the existing results，the nonlinear guaranteed costcontroller of this paper is nonlinear and the nonlinear guaranteed cost control law of system ispresented in terms of the solutions of LMIs.4. The problem of delay-dependent H∞control for Lurie systems with state and controlinput is investigated. By means of Lyapunov function and delay decomposition method. asufficient condition for the given systems with asymptotic stabilizable and H∞propertiescontroller is presented in term of a certain linear matrix inequality，and the desingning methodof the order memory state feedback H∞controllers is obtained.