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arXiv · 1603.03477

Stability Analysis of Networked Systems Containing Damped and Undamped Nodes

Filip Koerts·Mathias Bürger·Arjan van der Schaft·Claudio De Persis
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Abstract

This paper answers the question if a qualitatively heterogeneous passive networked system containing damped and undamped nodes shows consensus in the output of the nodes in the long run. While a standard Lyapunov analysis shows that the damped nodes will always converge to a steady-state value, the convergence of the undamped nodes is much more delicate and depends on the parameter values of the network as well as on the topology of the graph. A complete stability analysis is presented based on an eigenvector analysis involving the mass values and the topology of both the original graph and the reduced graph obtained by a Kron reduction that eliminates the damped nodes.

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Filip Koerts, Mathias Bürger, Arjan van der Schaft, Claudio De Persis. 2016-03-10. Stability Analysis of Networked Systems Containing Damped and Undamped Nodes. https://arxiv.org/abs/1603.03477

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