Robust Sliding Mode Synchronization under Periodic External Disturbances with Applications to Dumbell Satellite System

In this manuscript, we have obtained Generalized robust synchronization in identical chaotic systems, each starting from slightly different initial conditions. Sliding mode control technique is used to obtain complete synchronization, anti-synchronization, projective synchronization and hybrid projective synchronization between the identical chaotic systems which are subjected to periodic external disturbances as well. We show that on the switching surface, the controllers are also successful in achieving exponential synchronization. As a real-world example, the method is applied to two identical Dumbell satellite models, their initial conditions being only slightly different. We have applied the proposed control technique on them and have shown that generalized synchronization is achieved on the models. Thus, the motion of the trajectories of both the Dumbell Satellite systems are synchronized in future. Numerical simulations are performed on it to justify the theoretical analysis. An important application of synchronization of such satellites is the GPS (Global Positioning System) technology where motion of several satellites are synchronized together.