Observer-based synchronization in fractional-order leader–follower complex networks

This paper is devoted to synchronization behavior of complex dynamical networks with a Caputo fractional-order derivative. In particular, we propose a fractional-order leader–follower complex network where the leader is independent, has its own dynamics, and is followed by all the other nodes. Using the state observer approach, the leader and the followers are designed to connect through only a scalar coupling signal instead of the commonly used full state coupling scheme. On the basis of stability theory of the fractional-order differential system, a sufficient condition for global network synchronization is presented, which only relates to the linear part of individual nodes and can be easily solved by the pole-placement design technique. The analytic results are complemented with numerical simulations for a network whose nodes are governed by the fractional-order Chua’s circuit.