Adaptive synchronization of two different chaotic systems containing mutually Lipschitz nonlinearities subject to state time-delays

This article addresses the synchronization problem for two different chaotic systems with state time-delays, disturbances, and mutually Lipschitz nonlinearities. For analysis of the two different kind of chaotic oscillators, adaptive control theory, mutually Lipschitz condition and linear matrix inequalities (LMIs) based methodology are utilized to suppress the synchronization error and mismatch between the master-slave chaotic in the presence of disturbances and state delays. A novel adaptive control scheme for the synchronization of such systems is established that guarantees the convergence of the error trajectory and ensures the stability of the synchronization error system. In the end, established adaptive control law is verified by a numerical example of two different, popular in electronics, chaotic Chua´s circuit and Rossler system.