Observer Based on Sliding Mode Variable Structure for Synchronization of Chaotic Systems

In the paper an approach, based on the state observer of sliding mode variable structure, is used for synchronizing chaotic systems. It does not require either the computation of the Lyapunov exponents, or the initial conditions belonging to the same basin of attraction as the existed approaches based on the state observer for synchronizing chaotic systems. The approach is more robust against noise and parameter mismatch than the existed approaches based on the state observer for synchronizing chaotic systems, because the former uses variable structure control, which is strong robust with respect to noise and parameter mismatch in the error dynamics, the later uses an appropriate choice of the feedback gain. Two wellknown chaotic systems, a chaotic Rssler system and a hyperchaotic Rssler system are considered as illustrative examples to demonstrate the effectiveness of the used approach by numerical simulations. 