Lurie Delay Systems Synchronization Control

In this paper, synchronization control of Lurie system with time-delay has been considered. In view of different design of controller, several new delay-independent and delay-dependent sufficient conditions for the absolute stability of its error system, Lurie system with time-delay, have been driven in terms of linear matrix inequality (LMI) by using the Lyapunov stability theory, the matrix theory, the free power matrix, the Leibniz-Newton formula, the linear matrix inequality (LMI) approach, the Schur lemma as well as the corresponding inequality skill, the linear matrix inequality (LMI) can be easily solved by using Matlab toolbox.Concrete contents are as follows:1. Considering of the proportional controller with time-delay, several new delay-independent and delay-dependent absolute stability criterions of Lurie system with time-delay have been given in terms of linear matrix inequality by using Lyapunov functional, the Schur lemma, the free power matrix, the Leibniz-Newton formula and corresponding inequality skills. An example is given to illustrate the effectiveness of the method. Our result is less conservative.2. Considering of the PD controller with time-delay, several new delay-independent and delay-dependent absolute stability criterions of Lurie system with time-delay have been given in terms of linear matrix inequality by using Lyapunov functional, stability theory of operator, integral inequality, Schur lemma and free power matrix. Then, we have studied the case of no time-delay on the base of thses discussions, namely, the synchronization control of Lurie system without time-delay. The result has been solved by using the Matlab toolbox.3. Considering of the Lurie system with time-varying delay, the impusive controller has been studied on the base of stability theory of impusive differential equation. By using Lyapunov functional, free power matrix and Leibniz-Newton formula approach, the sufficient conditions for the global exponential stability of Lurie system with time-varying delay has been given. Based on the sufficient conditions, we have driven the impulsive synchronization of Lurie systems.