Synchronization of discrete-time CDNs via delayed impulsive control

This paper investigates the delayed impulsive control for synchronization of discrete-time complex dynamical networks (CDNs). The original dynamical network is complex with respect to the unstable or chaotic nodes, coupling time-delays, and time-varying, and thus it does not have the synchronization property. A synchronization scheme of impulsive control with delayed signal inputs is proposed for the discrete-time CDNs via hybrid discrete-time. By utilizing methods such as matrix spectrum and eigenvalue theory and dwell time, global uniform exponential stability (GUES) criteria are derived for the error system, under which exponential synchronization is achieved for the CDN. Moreover, by only delayed impulsive control signals, the exponential synchronization is realized for the CDN with coupling time-delays. Finally, two examples with numerical simulations are worked out for illustration.