Open AccessPinning synchronisation in fixed and switching directed networks of Lorenz‐type nodes
Author(s) -
Wen Guanghui,
Yu Wenwu,
Zhao Yu,
Cao Jinde
Publication year - 2013
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.2013.0090
Subject(s) - topology (electrical circuits) , network topology , node (physics) , dwell time , spanning tree , control theory (sociology) , mathematics , complex network , lyapunov stability , coupling strength , coupling (piping) , computer science , control (management) , discrete mathematics , physics , computer network , engineering , combinatorics , artificial intelligence , medicine , mechanical engineering , clinical psychology , quantum mechanics , condensed matter physics
This study addresses the global pinning synchronisation of directed networks with Lorenz‐type node dynamics. By using tools from M ‐matrix theory and Lyapunov stability theory, the interesting issues of what kind of nodes should be pinned and how large the control strength between neighbouring nodes should be selected for achieving global synchronisation in both fixed and switching networks are clearly addressed. It is theoretically shown that global pinning synchronisation of an arbitrarily given fixed network can be achieved if the network topology contains a directed spanning tree and the coupling strength is larger than a derived critical value depending both on the node dynamics and the network topology. By suitably constructing multiple Lyapunov functions, it is further proved that global pinning synchronisation in switching networks with a suitable coupling strength can be guaranteed if each possible network topology contains a directed spanning tree and the dwell time of switching is less than a positive threshold. Numerical examples are finally given for illustration.