Time-synchronized predefined-time synchronization between two non-identical chaotic systems

A new technique is proposed in this paper to synchronize chaotic systems. A time-synchronized predefined-time sliding mode control is designed such that the error dynamics between the drive and response systems converge to the origin simultaneously and within the predefined time. To realize the proposed notion of stability, a new sliding surface is introduced, and control laws are defined. The stability of the error dynamics and sliding surfaces is proved in the sense of Lyapunov by considering the effect of both smooth and non-smooth disturbances. Subsequently, two recently developed chaotic systems are successfully synchronized using the designed controller. A multi-wing chaotic system and a two-wing chaotic system are, respectively, taken as the drive and the response systems, and there is the coexistence of attractors in both systems. Further, the efficacy of the controller is validated using MATLAB simulations.