Adaptive observers-based synchronization of a class of Lur'e systems with delayed outputs for chaotic communications

In this paper, we propose an adaptive observer-based synchronization approach for a class of chaotic Lur'e systems with slope restricted nonlinearities and delayed outputs. The delay is assumed bounded and time varying and the information to be transmitted is assumed piecewise constant. Based on the Lyapunov-Krasovskii approach, we show that for sufficiently small values of the time-delay upper bound, both synchronization and information reconstruction objectives are ensured under a condition of persistent excitation and after solving a convex optimization problem. The result is illustrated via a numerical example of a chaotic communication system subject to a transmission delay.