Bounded synchronisation of singularly perturbed complex network with an application to power systems

Abstract

This study is concerned with the bounded synchronisation of singularly perturbed complex network. If the reduced network is boundedly synchronised, the authors obtain, by using partially contracting theory, an explicit bound for small perturbation parameter to guarantee the bounded synchronisation of singularly perturbed complex network. Moreover, the authors present a sufficient condition such that the reduced network is boundedly synchronised. Although this sufficient condition is difficult to test directly for general networks, it can be tested for power networks based on some existing results. The effectiveness of the proposed results is demonstrated via power networks.