Hilger-type impulsive differential inequality and its application to impulsive synchronization of delayed complex networks on time scales

The synchronization and synchronous control of complex networks [1] have rich dynamics and are lately receiving much needed attention [2–6]. Owing to the major role that impulsive control plays [6] in investigating synchronization problems and impulsive synchronization in dynamical networks, researchers have devoted more time researching them [2–6]. However, most of the existing literature concerning impulsive effects are confined to continuous or discrete time domains [2,6]. In this article, we establish Hilger-type impulsive differential inequality [7] which is a useful technical tool in investigating complex dynamic systems under impulsive disturbances. Meanwhile, we obtain scale-type synchronization criteria for complex networks with multiple delays. Our results not only improve existing results but also offer a new approach to understand the similarities and differences between synchronization of continuoustime and discrete-time cases, under impulsive effects.