Sponsor
I. Herman was supported by the Czech Science Foundation within the project GACR 13-06894S, J.J.P. Veerman's research was partially supported by the European Union's Seventh Framework Program (FP7-REGPOT-2012-2013-1) under grant agreement n316165
Document Type
Post-Print
Publication Date
2015
Subjects
Topology, Lapalcian matrices, Circular data, Multiagent systems -- Stability, Numerical integration
Abstract
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.
DOI
10.1016/j.ifacol.2015.10.324
Persistent Identifier
http://archives.pdx.edu/ds/psu/17778
Citation Details
Herman, Ivo; Martinec, Dan; Veerman, J. J. P.; and Sebek, Michael, "Stability of a Circular System With Multiple Asymmetric Laplacians" (2015). Mathematics and Statistics Faculty Publications and Presentations. 135.
http://archives.pdx.edu/ds/psu/17778
Description
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: http://dx.doi.org/10.1016/j.ifacol.2015.10.324