Journal
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
Volume 58, Issue 6, Pages 1358-1371Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSI.2010.2097670
Keywords
(Semi-)passive systems; delays; networks; nonlinear systems; synchronization
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We consider networks with a general topology which consist of nonlinear systems that interact via diffusive coupling with constant time-delays. Using the notion of (semi-)passivity we prove under some mild assumptions that passive systems will synchronize and that the solutions of interconnected semi-passive systems will be bounded. Furthermore we prove that identical strictly semi-passive systems, whose internal dynamics are stable, always will synchronize given that the coupling between the systems is sufficiently strong and a possible constant time delay is sufficiently small. We demonstrate our results using numerical simulations of a network consisting of linear systems and a network consisting Hindmarsh-Rose neurons.
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