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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
A Primer On Laplacian Dynamics In Directed Graphs, J. J. P. Veerman, R. Lyons
A Primer On Laplacian Dynamics In Directed Graphs, J. J. P. Veerman, R. Lyons
Mathematics and Statistics Faculty Publications and Presentations
We analyze the asymptotic behavior of general first order Laplacian processes on digraphs. The most important ones of these are diffusion and consensus with both continuous and discrete time. We treat diffusion and consensus as dual processes. This is the first complete exposition of this material in a single work.
Stability Of A Circular System With Multiple Asymmetric Laplacians, Ivo Herman, Dan Martinec, J. J. P. Veerman, Michael Sebek
Stability Of A Circular System With Multiple Asymmetric Laplacians, Ivo Herman, Dan Martinec, J. J. P. Veerman, Michael Sebek
Mathematics and Statistics Faculty Publications and Presentations
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 …