Decentralized guaranteed cost dynamic control for synchronization of a complex dynamical network with randomly switching topology

This paper considers synchronization problem of a complex dynamical network with randomly switching topology which means that the topology of a complex network probabilistically switches. For this problem, a decentralized guaranteed cost dynamic feedback controller is designed to achieve the synchronization of the network. Based on Lyapunov stability theory and linear matrix inequality framework, the existence condition for feasible controllers is derived in terms of linear matrix inequalities. Finally, the proposed method is applied to two numerical examples in order to show the effectiveness of our result.