DISCRETE AND CONTINUOUS doi:10.3934/dcdsb.2011.16.1071 DYNAMICAL SYSTEMS SERIES B Volume 16, Number 4, November 2011 pp. 1071–1082 SYNCHRONIZATION OF CHAOTIC SYSTEMS WITH TIME-VARYING COUPLING DELAYS Tingwen Huang Texas A&M University at Qatar Doha, P.O.Box 23874, Qatar Guanrong Chen Department of Electronic Engineering City University of Hong Kong Hong Kong, China Juergen Kurths Institute for Physics, University of Potsdam Am Neuen Palais, Gebude 19, D-14415 Potsdam, Germany Dedicated to the 65th Birthday of Professor Kok Lay Teo Abstract. In this paper, we study the complete synchronization of a class of time-varying delayed coupled chaotic systems using feedback control. In terms of Linear Matrix Inequalities, a sufficient condition is obtained through using a Lyapunov-Krasovskii functional and differential equation inequalities. The conditions can be easily verified and implemented. We present two simulation examples to illustrate the effectiveness of the proposed method. 1. Introduction. In this paper, we address the complete synchronization of a class of time-varying delayed chaotic systems. Chaos synchronization is a basic focus in nonlinear science due to its extensive applications in secure communications, biolog- ical science, neural networks, automatic control, etc. Since the 1990s, chaos control and synchronization have sparked increasing interest of many researchers, and many schemes have been developed. The readers are referred to the review monographs [1],[6], where the authors presented the main ideas involved in the field of chaos synchronization as well as many potential applications. So far, a lot of research on this subject has been done, and many fundamental results have been reported on synchronization and control of chaotic systems by scholars from physics, engineer- ing, biology, and mathematics, etc. Various control schemes have been developed to synchronize chaotic systems such as drive-response, coupling control, adaptive control, feedback control, observer-based control, impulsive control, intermittent control, to name some typical ones. Many delayed systems in various research fields including biology, chemistry, nonlinear optics, economics, and epidemiology, have been found to be chaotic. For 2000 Mathematics Subject Classification. Primary: 34A20, 34G20. Key words and phrases. Synchronization, Chaotic System, Time-varying Delay. The work described in this paper was partially supported by the National Natural Science Foundation of China (Grant No. 60974020 and No. 10971240), and by the Hong Kong RGC under the GRF Grant CityU1114/11E. . 1071