Open AccessFinite‐time cluster synchronisation of Markovian switching complex networks with stochastic perturbations
Author(s) -
Cui Wenxia,
Fang Jianan,
Zhang Wenbing,
Wang Xin
Publication year - 2014
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.2013.0370
Subject(s) - robustness (evolution) , control theory (sociology) , convergence (economics) , markov process , stochastic process , mathematics , computer science , stability (learning theory) , cluster (spacecraft) , lyapunov function , mathematical optimization , control (management) , nonlinear system , biochemistry , chemistry , statistics , artificial intelligence , machine learning , economics , gene , programming language , economic growth , physics , quantum mechanics
In this study, the authors study the finite‐time cluster synchronisation problem for a class of Markovian switching complex networks with stochastic noise perturbations. By constructing the suitable stochastic Lyapunov–Krasovskii functional, using finite‐time stability theorem, inequality techniques and the properties of Weiner process, sufficient conditions are obtained to ensure finite‐time cluster synchronisation for the complex networks with or without time delays. The effects of control parameters on cluster synchronisation speed and time delays are also analysed. Since finite‐time cluster synchronisation means the optimality in convergence time and has better robustness and disturbance rejection properties, this study has important theory significance and practical application value. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results.