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Published July 2013 | public
Journal Article

Optimization of convergence rate and stability margin of information flow in cooperative systems

Abstract

The interplay between the convergence rate and stability margin (e.g. ability to reject disturbances) for a discrete-time information flow filter in cooperative systems is analyzed. For a given communication graph, the convergence rate is defined as the absolute value of the largest nonunit characteristic root of a matrix associated with the filter. The maximal convergence rate, obtained by "tuning" the control gains, is highly correlated to the number of distinct eigenvalues of the graph Laplacian (it is 1 for the complete graph). A stability margin is introduced for multiple-input–multiple-output (MIMO) systems and is then maximized with respect to the control gains subject to a constraint on the convergence rate. The optimal stability margin as a function of the convergence rate is bounded above for any order of the filter, and the bound is attained for the complete graph. For the zero-order filter and all strongly connected communication graphs, the optimal stability margin is found analytically, whereas for the first-order filter and undirected communication graphs, it is evaluated numerically. The results demonstrate the ability to distinguish graph topologies that dominate others in their ability to reject disturbances and converge rapidly to a consensus.

Additional Information

© 2013 Elsevier Ltd. Received 11 October 2011; Received in revised form 15 January 2013; Accepted 13 March 2013; Available online 25 April 2013. The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Wei Ren under the direction of Editor Frank Allgöwer. We are grateful to the anonymous referees for their valuable comments and suggestions, which greatly helped us to improve the quality of the paper.

Additional details

Created:
August 22, 2023
Modified:
October 24, 2023