Synchronization of the chaotic fractional-order multi-agent systems under partial contraction theory

In this paper, a new synchronization criterion for leader-follower fractional-order chaotic systems using partial contraction theory under an undirected fixed graph is presented. Without analyzing the stability of the error system, first the condition of partial contraction theory for the synchronization of fractional systems is explained, and then the input control vector is designed to apply the condition. An important feature of this control method is the rapid convergence of all agents into a common state. Finally, numerical examples with corresponding simulations are presented to demonstrate the efficiency and performance of the stated method in controlling fractional-order systems. The simulation results show the appropriate design of the proposed control input.