State synchronization of controlled nodes via the dynamics of links for complex dynamical networks

A continuous time-varying complex dynamical network with the graph model may be regarded to be composed of two interconnected subsystems, one of which is the nodes subsystem (NS) and the other is the links subsystem (LS). The two subsystems can be modeled mathematically by the state differential equations, in which the weighted values of links are regarded as the state variables of LS. This paper mainly focuses on the dynamics of LS, which is modeled as the Riccati matrix differential equation, and investigates the state synchronization of NS associated with the synthesized state feedback controller for NS and the constructed coupling relation in LS. Firstly, this paper proposes the equivalent condition of state synchronization by using the matrix algebra method. Then, the state feedback controller for NS is proposed and the coupling relation in LS is also constructed based on the Lyapunov stability theory, by which the asymptotic state synchronization of NS is sure to be realized. Finally, numerical simulations are given to verify the effectiveness of the theoretical results in this paper. (C) 2019 Published by Elsevier B.V.