Synchronization of chaotic systems with unknown time delay by sliding mode observer approach and unknown delay identification

In secure communication applications, time-delayed chaotic systems in comparison with simple chaotic systems have higher security level. So in this paper synchronization of time-delayed chaotic systems is investigated. A Sliding Mode Observer (SMO) based method is used for synchronization. In addition, for more security in communication, delay of drive system (transmitter) is supposed to be unknown to response system (receiver). Sliding mode observer just compensates the uncertainties in nonlinear part, but unknown time delay exists in linear part of the system. So the designed sliding mode observer cannot provide accurate estimates of states. It is proposed that unknown delay being identified using estimated states by the observer. For this purpose, system model is rewritten in terms of delayed states and these delayed states are achieved by solving this equation. Eventually, the cross correlation function is computed between the delayed states and states estimated by the observer. The value that corresponds to maximum of this cross correlation function is the estimated time delay. After delay estimation, the observer can use it in synchronization of the chaotic systems.