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Stability of a Circular System With Multiple Asymmetric Laplacians
Mathematics and Statistics Faculty Publications and Presentations
  • Ivo Herman, Czech Technical University, Prague
  • Dan Martinec, Czech Technical University, Prague
  • J. J. P. Veerman, Portland State University
  • Michael Sebek, Czech Technical University, Prague
Document Type
Publication Date
  • Topology,
  • Lapalcian matrices,
  • Circular data,
  • Multiagent systems -- Stability,
  • Numerical integration
We consider an asymptotic stability of a circular system where the coupling Laplacians are different for each state used for synchronization. It is shown that there must be a symmetric coupling in the output state to guarantee the stability for agents with two integrators in the open loop. Systems with agents having three or more integrators cannot be stabilized by any coupling. In addition, recent works in analysis of a scaling in vehicular platoons relate the asymptotic stability of a circular system to a string stability. Therefore, as confirmed by simulations in the paper, our results have an application also in path graphs.

This is the author’s version of a work that was accepted for publication in IFAC-PapersOnLine. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.

A definitive version was subsequently published in IFAC-PapersOnLine and can be found online at:

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Citation Information
Ivo Herman, Dan Martinec, J. J. P. Veerman and Michael Sebek. "Stability of a Circular System With Multiple Asymmetric Laplacians" (2015)
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