Delayed state-feedback control for synchronization of complex networks with coupling delays and impulsive disturbances

Abstract

This paper concentrates on the synchronization problem of complex networks subject to coupling delays and impulsive disturbances, employing delayed state-feedback control strategies. By constructing a Lyapunov–Krasovskii functional with two different exponential decay rates, the complex networks with impulsive disturbances can achieve globally exponential synchronization (GES). Furthermore, the derived synchronization norms establish a link between coupling delay and feedback delay. This paper considers the normal situation in which the control term is expressed as $B_i{u}_i$, where $B_i$ is a common $n\times m$ real matrix. Tackling this type of issue poses greater challenges than dealing with the special case where $B_i$ is an identity matrix. Through appropriate selection of matrix $B_i$, the controller can be effectively employed across all or certain states. To demonstrate the practical validity of the proposed approach, a numerical example is presented to illustrate its effectiveness.