Stability And Robust H_∞ Control Of Uncertain Time-delay Systems

Abstract Time-delay is a phenomenon of nature, and it exists widely and cannot be avoided. It is very important to study the phenomenon in resolving the retard in engineering and improving the performance of control systems. Stability is the premise of normal work for practical systems, so the stability of time-delay systems is noticed, lately. By constructing Lyapunov functional, this paper proposed the sufficient conditions to guarrantee asymptotic stability for uncertain neutral systems with time delays on basis of Lyapunov stable theory.The control theory for systems has been investigated well in robust control theory. For so-called robust H∞control, its aim is to design a controller for the given system, such that for all admissible uncertainty the closed-loop system satisfies:(i) The closed-loop system is uniformly asympotically stable.(ii) The H∞norm of the transfer function Tωz(S) from disturbancesωto controlled ouput z satisfies‖Tωz(s)‖∞＜rOn the basis of LMIs, this paper proposed the conditions for uncertain neutral time- delay systems with time delay in control input. At the same time, when the derivate of state is zero, robust control of nonlinear time-delay systems is considered and the state feedback robust H∞controller is designed by the solutions of the LMIs.The main contents in this paper are as follows:(1) Stability of uncertain neutral time-delay system is considered. Firstly, an operator is defined, then a new Lyapunov functional is constructed in terms of the above defined operator. By Lyapunov stability theory, the sufficient conditions to robust asymptotic stability of the nominal system are presented. Furthermore, we generalize the results to uncertain system. Using Leibniz-Newton formula, this paper take the size of the neutral- and discrete-delays into account. Since the neutral-delay and disctete-delay influence each other, our criterion is less conservative than previous. Finally, numerical examples demenstrate that the proposed criterion is feasible and less conservative. (2) Robust H∞control of uncertain neutral system with time delay in control input is investigated. By Lyapunov stability theory and a integral inequality, the derivate of Lyapunov function is properly enlarged. Finally, conditions to the state feedback controller and its design method are presented in terms of LMIs, which ensur the closed-loop system has H∞permance.(3) Robust H∞control for a class of uncertain nonlinear time-delay systems is studied. Fistly, constructing Lyapunov functional and properly enlarging inequality, problems are sloved by LMI techniques. The state feedback law is gaiven based on the solutions of LMIs. Finally, the design method of H∞controller is presented.