State‐dependent impulsive synchronisation of complex dynamical networks with non‐linear coupling

This study investigates the synchronisation problem for complex dynamical networks with non‐linear coupling via state‐dependent impulsive control. In contrast to most existing publications, impulses occurring are not at fixed instants but depend on the states of each node. Based on the differential mean value theorem and inequality techniques, several sufficient conditions with theoretical demonstration ensuring every solution of the error nodes intersect each surface of the discontinuity exactly once are derived. Moreover, by applying the B‐equivalence method, the error system with state‐dependent impulses can be reduced to the fixed‐time impulsive ones, which can be analysed via Lyapunov stability theory and mathematical induction. Finally, two numerical examples are carried out to demonstrate the performance of the obtained results.