Stabilization of a class of dynamical complex networks based on decentralized control

This paper deals with a stabilization problem for a class of dynamical complex networks with each node being a general Lur'e system. Based on a Lur'e-Postnikov function and a special decentralized control strategy, the problem of designing a linear feedback controller such that states of all nodes are globally stabilized onto an expected homogeneous state is addressed. A controller design method based on parameter-dependent Lur'e-Postnikov function is proposed in order to reduce the conservativeness and the controller can be constructed via feasible solutions of a certain set of linear matrix inequalities (LMIs). A dynamical network composed of identical Chua's circuits is adopted as a numerical example to demonstrate the effectiveness of the proposed results.