Adaptive Predefined-Time Synchronization of Two Different Fractional-Order Chaotic Systems With Time-Delay

This paper devotes to the adaptive globally synchronization within predefined-time of two time-delayed fractional-order chaotic systems. Firstly, through fractional calculus, two novel different fractional-order systems with time-delay are proposed, whose convergence is guaranteed and phase trajectory is given. Secondly, by exploiting the non-negative Lyapunov function and inequality theorem, a novel global predefined-time stability theorem is proposed, which can ensure the settling time tunable. And the upper bound of the settling time estimation is more accurate compared with the classical results. With the help of novel predefined-time stability theorem, two active controllers are designed, namely the fixed-time synchronization controller and predefined-time synchronization controller, to achieve the fixed-time synchronization and the predefined-time synchronization of two different time-delayed fractional-order chaotic systems respectively. Finally, several numerical simulations are presented in order to show the effectiveness of the proposed methods.