Open AccessCluster synchronisation in non‐linearly coupled impulsive networks with non‐identical nodes and time‐varying delays
Author(s) -
Fan Hongguang,
Zhao Yi,
Feng Jianwen
Publication year - 2016
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.2015.0690
Subject(s) - control theory (sociology) , generality , cluster (spacecraft) , mathematics , topology (electrical circuits) , stability (learning theory) , linear matrix inequality , coupling (piping) , matrix (chemical analysis) , complex network , computer science , mathematical optimization , control (management) , engineering , combinatorics , mechanical engineering , psychology , materials science , artificial intelligence , machine learning , composite material , psychotherapist , programming language
This study investigates cluster synchronisation of non‐linearly coupled impulsive networks with time‐varying delay. Without loss of generality, it is assumed that the nodes in the networks to be non‐identical and the coupling matrix to be asymmetric. Two kinds of topological structures are concerned, which correspond to positive weighted network, as well as cooperative and competitive network, respectively. Pinning controllers are designed in order to achieve cluster synchronisation. According to the Lyapunov stability theory, impulsive delay differential inequalities and linear matrix inequalities, some criteria for cluster synchronisation of non‐linear impulsive dynamical systems are obtained. Two numerical examples are given to demonstrate the effectiveness of the authors' new results.