A novel fast terminal sliding mode with predefined-time synchronization

This paper aims to investigate the predefined-time synchronization analysis for two different multiple-inputmultiple-output systems. Firstly, based on the definition of predefined-time synchronization, we propose a novel Lyapunov function and a novel fast terminal sliding mode, each having corresponding sufficient conditions for predefined-time synchronization. Second, we respectively derive the novel fast terminal sliding mode controllers for synchronization schemes with and without taking into account the uncertainty. The desired convergence time can be obtained by setting predefined-time parameters Tpi in advance. Finally, the controllers and the corresponding parameters designed for comparison are applied to predefined-time synchronization of two chaotic systems. The efficacy and robustness of the obtained results are demonstrated by numerical simulations.