Synchronisation of discrete-time complex networks with delayed heterogeneous impulses

In this study, the synchronisation problem is investigated for discrete-time complex networks with delayed heterogeneous impulses. Heterogeneous impulses are a form of inhomogeneous impulse, which means that the impulsive strengths depend on both time and space domains. To describe more appropriately impulsive effects, both heterogeneous impulsive effects and impulsive input delays are considered. Employing the Razumikhin theorem and constructing a time-dependent Lyapunov function, several sufficient criteria are derived to ensure exponential synchronisation of the discrete-time complex networks with delayed heterogeneous impulsive effects. The derived criteria are formulated in terms of linear matrix inequalities, in which the impulsive intervals, impulsive input delays and impulsive strengths play an important role. Finally, an example is delivered to illustrate the effectiveness of the proposed synchronisation criteria.