Pinning control for cluster synchronisation of complex dynamical networks with semi-Markovian jump topology

In this paper, a pinning controller is designed for cluster synchronisation of complex dynamical networks with semi-Markovian jump topology, which covers the concept of the conventional Markovian jump as a special case. To decide on the pinned-node for the cluster synchronisation, a novel procedure is proposed based on a topological structure. In addition, criteria for the synchronisation are separately derived for the controller with the mode-independent and mode-dependent pinned-node, respectively. A practical example is given to illustrate the effectiveness of the proposed methods.