Abstract
In this paper, we consider synchronization of N identical nonlinear systems unidirectionally or bidirectionally coupled with time delay. First we show, using the small-gain theorem, that trajectories of coupled strictly semi-passive systems converge to a bounded region. Next, we consider the network structure under which the synchronization error dynamics has a trivial solution at zero and derive a necessary condition for synchronization with respect to the network structure. Using these facts, we then derive sufficient conditions for synchronization of the systems in terms of linear matrix inequalities via the Lyapunov-Krasovskii functional approach. The obtained results are illustrated on networks of Lorentz systems with coupling delay.
Original language | English |
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Article number | 037108 |
Number of pages | 14 |
Journal | Chaos |
Volume | 18 |
Issue number | 3 |
DOIs | |
Publication status | Published - 22 Sept 2008 |
Bibliographical note
Funding Information:This work was supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (No. 18560441).
Funding
This work was supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (No. 18560441).