Synchronization criteria of chaotic Lur׳e systems with delayed feedback PD control

This paper is concerned with the problem of global asymptotical synchronization of chaotic Lur׳e systems by using a delayed feedback proportional-derivative (PD) control scheme. Based on Lyapunov functional approach, a stabilization condition for the synchronization error systems with delayed PD control is derived. The designed delayed PD feedback controller can ensure that the master and slave systems are asymptotically synchronous. The advantage of the constructed Lyapunov functional lies in the fact that it makes full use of the additional derivative state term. Furthermore, a less conservative synchronization criterion is proposed for the considered system only used proportional control. Compared with the existing ones, the merit of the proposed results in this paper lies in their reduced conservatism and application of the derivative control. The conditions represented in terms of linear matrix inequalities (LMIs) can be solved by the application of convex optimization algorithms. Finally, numerical examples are given to show the effectiveness of the proposed method and the improvement over some existing results.