On Stability and Inverse Optimality for a Class of Multi-agent Linear Consensus Protocols

Keun Uk Lee, Jae Young Lee, Yoon Ho Choi, Jin Bae Park

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


This paper studies stability and inverse optimality for a class of linear consensus protocols applied to the identical linear time-invariant multi-agent systems, where communications among the agents are described by a fixed digraph, containing a spanning tree, whose scaled Laplacian is diagonalizable. The concept of the scaled Laplacian, normal Laplacian multiplied by a positive diagonal matrix, allows a more general graph topology to be handled. First, we show that partial stability and, even more, inverse optimality hold if either the scaling factors in each protocol are sufficiently large depending on graph properties, or the system matrix A satisfies the Lyapunov inequality. Then, duality principles between the agents’ and the consensus error dynamics are presented, which provide additional properties regarding consensus-related stability and inverse optimality. And the results are characterized in terms of the related symmetric Laplacian and its algebraic connectivity when the given graph is scaled undirected. Finally, through formation control simulation of a multi-agent mobile robot system for Г-scaled undirected and Г-scaled directed graphs, we have verified the theory of this paper on the partial stability and the inverse optimality conditions.

Original languageEnglish
Pages (from-to)1194-1206
Number of pages13
JournalInternational Journal of Control, Automation and Systems
Issue number3
Publication statusPublished - 2018 Jun 1

Bibliographical note

Funding Information:
Manuscript received November 21, 2016; revised September 1, 2017; accepted November 13, 2017. Recommended by Associate Editor Juhoon Back under the direction of Editor Yoshito Ohta. This work has been supported by National Research Foundation of Korea Grant funded by the Korean Government (No. 2013R1A1A2012851).

Publisher Copyright:
© 2018, Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature.

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications


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