Open AccessAlmost sure exponential synchronisation of networked harmonic oscillators via intermittent coupling subject to Markovian jumping
Author(s) -
Wang Jingyi,
Feng Jianwen,
Xu Chen,
Zhao Yi
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.0951
Subject(s) - jumping , control theory (sociology) , coupling (piping) , synchronization (alternating current) , markov process , exponential function , harmonic , computer science , exponential distribution , mathematics , statistical physics , physics , topology (electrical circuits) , engineering , mathematical analysis , artificial intelligence , control (management) , quantum mechanics , statistics , combinatorics , physiology , mechanical engineering , biology
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.