Cluster Synchronization in Switched Complex Dynamical Networks Using Delayed Pinning Impulsive Control

This paper explores cluster synchronization in switched complex networks by employing a delayed pinning impulsive control strategy rigorously derived via contraction theory. Unlike traditional methods that require impulsive control to occur synchronously with switching events, our approach allows impulsive actions to occur independently by incorporating mode-dependent impulsive effects. In particular, the concept of a mode-dependent average impulsive interval (MDAII) is used, which assigns distinct impulsive intervals to each mode, thereby enhancing control flexibility and efficiency. Moreover, by accounting for both system and coupling delays and combining the MDAII with a mode-dependent average dwell time (MDADT) strategy, we derive a set of Lyapunov functionals that rigorously establish synchronization criteria in terms of impulsive control gains, delay parameters, and mode transitions. The efficacy of the proposed framework is demonstrated through numerical simulations involving synchronization in artificial neural networks and Hindmarsh-Rose neuronal oscillators, thus, demonstrating its practical applicability.