Adaptive Modified Hybrid Robust Projective Synchronization Between Identical and Nonidentical Fractional Order Complex Chaotic Systems With Fully Unknown Parameters

Abstract

In this paper, a robust adaptive sliding mode controller is proposed. Under the existence of external disturbances, modified hybrid projective synchronization (MHPS) between two identical and two nonidentical fractionalorder complex chaotic systems is achieved. It is shown that the response system could be synchronized with the drive system up to a nondiagonal scaling matrix. An adaptive controller and parameter update laws are investigated based on the Lyapunov stability theorem. The closedloop stability conditions are derived based on the fractionalorder Lyapunov function and MittagLeffler function. Finally, numerical simulations are given to verify the theoretical analysis.