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
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.
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.