Almost sure exponential synchronisation of networked harmonic oscillators via intermittent coupling subject to Markovian jumping

• Published in: IET control theory & applications Vol. 12; no. 11; pp. 1658 - 1664
• Main Authors: Wang, Jingyi, Feng, Jianwen, Xu, Chen, Zhao, Yi
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 24.07.2018
• Subjects: Brief Paper; communication networks; complete synchronisation; complex networks; coupling network; coupling protocol; desired synchronisation trajectory; differential equations; directed graphs; exponential synchronisation; intermittent coupling subject; Lyapunov methods; Markov processes; Markovian jumping; networked harmonic oscillators; numerical analysis; periodical intermittent interactions; sampled velocity data; stochastic processes; strength; synchronisation; Markovian jumping; strength; communication networks; complex networks; networked harmonic oscillators; sampled velocity data; exponential synchronisation; differential equations; synchronisation; periodical intermittent interactions; coupling network; directed graphs; desired synchronisation trajectory; intermittent coupling subject; coupling protocol; numerical analysis; Markov processes; complete synchronisation; stochastic processes; Lyapunov methods
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2017.0951

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.