Almost sure exponential synchronisation of networked harmonic oscillators via intermittent coupling subject to Markovian jumping - Wang, Jingyi; Feng, Jianwen; Xu, Chen; Zhao, Yi (IET control theory & applications, 2018)
Synchronisation behaviours emerge from the interaction of oscillators. This study addresses the problem of almost sure exponential synchronisation for networked harmonic oscillators over switching communication networks. The coupling protocol relies on only the sampled velocity data and is periodical intermittent interactions over networks described by directed graphs subject to Markovian jumping. Next, the leader–following coupling protocol is proposed in order to approach a desired synchronisation trajectory. By using the stability theory of stochastic differential equations, some sufficient conditions are established to guarantee synchronisation in the almost sure sense. The almost sure exponential synchronisation can be achieved even when the coupling network and strength are switched between enabling and disabling the system to achieve complete synchronisation. Some numerical simulations are presented to illustrate the effectiveness of the theoretical results.