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On delay-induced stability in diffusively coupled discrete-time systems

Content Provider	Springer Nature Link
Author	Atay, Fatihcan M.
Copyright Year	2011
Abstract	The stability of networked systems is considered under time-delayed diffusive coupling. Necessary conditions for stability are given for general directed and weighted networks with both positive and negative weights. Exact stability conditions are obtained for undirected networks with nonnegative weights, and it is shown that the largest eigenvalue of the graph Laplacian determines the effect of the connection topology on stability. It is further shown that the stability region in the parameter space shrinks with increasing values of the largest eigenvalue, or of the time delay of the same parity. In particular, unstable fixed points of the individual maps can be stabilized for certain parameter ranges when they are coupled with an odd time delay, provided that the connection structure is not bipartite. Furthermore, signal propagation delays are compared to signal processing delays and it is shown that delay-induced stability cannot occur for the latter. Connections to continuous-time systems are indicated.
Starting Page	109
Ending Page	119
Page Count	11
File Format	PDF
ISSN	10129405
Journal	Afrika Matematika
Volume Number	23
Issue Number	1
e-ISSN	21907668
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-04-27
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Delay Stability Signed graph Synchronization Chaos Stability theory Applications of graph theory Signed and weighted graphs Mathematics Education Mathematics Applications of Mathematics History of Mathematical Sciences
Content Type	Text
Resource Type	Article
Subject	Mathematics

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