Smooth Control Steering Global Predefined-Time Synchronization for a Class of Nonlinear Systems

This letter addresses the problem of robust global predefined-time synchronization for a class of nonlinear systems, in which the settling-time is explicit compared with the conventional fixed-time synchronization. Specially, the designed control scheme is smooth, namely differentiable, which is distinguished from the traditional fast control methods containing the signum function. By the Lyapunov stability analysis, the sufficient criterion is derived for achieving the global predefined-time synchronization. More importantly, the obtained results have been directly applied into synchronizing two chaotic systems. Finally, the numerical simulation on predefined-time synchronization of chaotic systems is arranged for verifying the correction and effectiveness of theoretical results.