Master-slave synchronization of complex-valued delayed chaotic Lur’e systems with sampled-data control

Abstract

The master-slave synchronization of a type of the complex-valued chaotic Lur’e systems (CVCLSs) with time delay is addressed for the first time, with decomposing complex-valued dynamic systems into two real-valued systems. The complex-valued state variables are introduced in the chaotic Lur’e systems, which expand the application in image processing and remote operation control, and improve the confidentiality in secure communication. Firstly, on the basis of the Lyapunov principle, a Lyapunov-Krasovkii functional (LKF) is established by using certain novel augmented terms, which can take full advantage of the usable information on the sampled-data and the characteristics of the system. Secondly, in the case of a complex-valued delayed chaotic Lur’e system, a more general synchronization criterion is constructed to expand certain current conclusions in the real domain. What’s more, the required gain matrices can be designed according to the solution of the linear matrix inequalities (LMIs). In contrast, the conclusions of this paper are more extensive than some existing studies. At last, the validity of the conclusions of this paper is proved by numerical simulations.