Network topology and synchronization of systems with linear time-delayed coupling

E. Steur; H. Nijmeijer

doi:10.1007/978-3-319-20988-3_17

Network topology and synchronization of systems with linear time-delayed coupling

E. Steur, H. Nijmeijer

Dynamics and Control

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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Abstract

We consider networks of square input–output systems that interact via linear, time-delayed coupling functions. For given system dynamics, we give conditions for the construction of a (local, global) synchronization diagram. We show that a condition for (local, global) synchronization is that the coupling strength and time-delay are contained in the intersection of scaled copies of the (local, global) synchronization diagram, where the scaling factors are the nonzero eigenvalues of the symmetric Laplacian matrix.

Original language	English
Title of host publication	Mathematical Control Theory I
Subtitle of host publication	Nonlinear and Hybrid Control Systems
Editors	M.K. Camlibel , A.A. Julius, R. Pasumarthy , J.M.A. Scherpen
Place of Publication	Berlin
Publisher	Springer
Pages	321-341
Number of pages	21
ISBN (Electronic)	978-3-319-20988-3
ISBN (Print)	978-3-319-20987-6
DOIs	https://doi.org/10.1007/978-3-319-20988-3_17
Publication status	Published - 2015

Publication series

Name	Lecture Notes in Control and Information Sciences
Volume	461
ISSN (Print)	0170-8643

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10.1007/978-3-319-20988-3_17

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Steur, E., & Nijmeijer, H. (2015). Network topology and synchronization of systems with linear time-delayed coupling. In M. K. Camlibel , A. A. Julius, R. Pasumarthy , & J. M. A. Scherpen (Eds.), Mathematical Control Theory I: Nonlinear and Hybrid Control Systems (pp. 321-341). (Lecture Notes in Control and Information Sciences ; Vol. 461). Springer. https://doi.org/10.1007/978-3-319-20988-3_17

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abstract = "We consider networks of square input–output systems that interact via linear, time-delayed coupling functions. For given system dynamics, we give conditions for the construction of a (local, global) synchronization diagram. We show that a condition for (local, global) synchronization is that the coupling strength and time-delay are contained in the intersection of scaled copies of the (local, global) synchronization diagram, where the scaling factors are the nonzero eigenvalues of the symmetric Laplacian matrix.",

author = "E. Steur and H. Nijmeijer",

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Steur, E & Nijmeijer, H 2015, Network topology and synchronization of systems with linear time-delayed coupling. in MK Camlibel , AA Julius, R Pasumarthy & JMA Scherpen (eds), Mathematical Control Theory I: Nonlinear and Hybrid Control Systems. Lecture Notes in Control and Information Sciences , vol. 461, Springer, Berlin, pp. 321-341. https://doi.org/10.1007/978-3-319-20988-3_17

Network topology and synchronization of systems with linear time-delayed coupling. / Steur, E.; Nijmeijer, H.
Mathematical Control Theory I: Nonlinear and Hybrid Control Systems. ed. / M.K. Camlibel ; A.A. Julius; R. Pasumarthy ; J.M.A. Scherpen. Berlin: Springer, 2015. p. 321-341 (Lecture Notes in Control and Information Sciences ; Vol. 461).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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AU - Nijmeijer, H.

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AB - We consider networks of square input–output systems that interact via linear, time-delayed coupling functions. For given system dynamics, we give conditions for the construction of a (local, global) synchronization diagram. We show that a condition for (local, global) synchronization is that the coupling strength and time-delay are contained in the intersection of scaled copies of the (local, global) synchronization diagram, where the scaling factors are the nonzero eigenvalues of the symmetric Laplacian matrix.

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A2 - Pasumarthy , R.

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PB - Springer

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Network topology and synchronization of systems with linear time-delayed coupling

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