Guaranteed Cost Control For Uncertain Systems With Time-Delays

With the development of the research on robust control, guaranteed cost control problems have drawn considerable attention. It can ensure dynamic closed-loop system is asymptotically stable, and the closed-loop cost function value is not more than a specified upper bound. In this paper, based on Lyapunov stability theory and the theory of Linear matrix inequalities (LMI),we studied the problems of guaranteed cost control for tow kinds of time-delay systems,namely, the uncertain discrete time-delay systems and uncertain singular time-delay systems.The main contents are as follows:Firstly , the sufficient condition of corresponding control law of uncertain discrete time-delay systems is given based on Lyapunov stability theory and the linear matrix inequality.Then,the numerical example is given to show the validity of our conclusion via the LMI-box.Secondly, focuses on a class of time-varying uncertain singular systems with both state and input delays, the problem of non-fragile H_∞guaranteed cost control is discussed. Suppose that the time-varying uncertain parameters are norm-bounded, but the matched conditions are not required to satisfy. A sufficient condition is given in terms of Lyapunov stability theory for the existence of the non-fragile H_∞guaranteed cost controllers. And a minimal value of cost function is derived.Finally, the problem of delay-dependent non-fragile robust H_∞control for uncertain singular systems with time-delay is studied. Based on an integral inequality method, a new H_∞delay-dependent condition, which can ensure that the closed-loop system is internally stable with a given H_∞disturbance attenuation level via a non-fragile controller, is obtained by using the Lyapunov-Krasovskii stability theory. Finally, a numerical simulation is given to show the validity of this approach.