Discrete sliding mode control for hybrid synchronization of continuous Lorenz systems with matched/unmatched disturbances

This paper is concerned with the hybrid synchronization of master-slave Lorenz systems with uncertainties. A new systematic design procedure to synchronize continuous master-slave Lorenz chaotic systems is proposed by using a discrete sliding mode control (DSMC). In contrast to the previous works, the design of DSMC can be simplified and only a single controller is needed to realize chaos synchronization. The proposed DSMC ensures the occurrence of the sliding mode. When the controlled system is in the sliding manifold, the effect of disturbances including matched and unmatched cases are discussed. The proposed results conclude the synchronization error of controlled master-slave systems with matched disturbances can be fully derived to zero or robustly suppressed in an estimated bound even with unmatched disturbances, which is not addressed in the literature. The numerical simulation results demonstrate the success and effectiveness of the proposed DSMC developed in this paper.