A novel observer-based chaos synchronization for secure communications

: In this paper, a new observer-based scheme for secure communication is proposed. It is consisted of a state space observer and a robustifying term using the responses of linear differential equations to compensate for the nonlinearities. In fact, it is assumed that the lumped uncertainty can be modeled by linear differential equations. Using the Stone-Weierstrass theorem, it is shown that response of this differential equations can approximate nonlinear functions. Adaptation rules are designed to estimate the parameters of the response function of the differential equation. The information signal is added to the output of a master chaotic system. This signal is transmitted to the receiver which is a state observer. Using Lyapunov stability theorem and Barbalat’s lemma, it is guaranteed that the observation error converges to zero and the information signal can be recovered. Simulation results reveal the effectiveness of the proposed method.