Synchronization for chaotic systems and chaos-based secure communications via both reduced-order and step-by-step sliding mode observers

This paper considers the problems of the chaos synchronization and chaos-based secure communication when the observer matching condition is not satisfied. An auxiliary drive signal vector which may satisfy the observer matching condition is constructed. By using the drive signals of original system, a step-by-step sliding mode observer is considered to obtain the exact estimates of the auxiliary drive signals and their derivatives. A reduced-order observer is designed to asymptotically estimate the states of the drive system. By using the estimates of states and the derivatives of the auxiliary signals, an information signal recovery method which does not use any derivative information of original drive system is developed. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.