Sliding mode control for synchronization of Rössler systems with time delays and its application to secure communication

This study is concerned with the chaos synchronization problem of Rössler systems subjected to multiple time delays. Based on the sliding mode control (SMC) technique, we first propose an adaptive switching surface which does not allow for a reduction of system order, as is the case in most SMC schemes. Then both a sliding mode controller and a new sufficient condition are derived to guarantee, respectively, the global hitting of the sliding mode and stability of the equivalent error dynamics in the sliding mode. Thus, the chaos synchronization for Rössler systems with multiple time delays can surely be achieved. Moreover, the proposed scheme is then applied to the secure communication system. Numerical simulations are included to demonstrate the feasibility of the proposed scheme.