Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2012-001 (January 12, 2012)

Robustness of consensus systems
by Kiyotsugu Takaba

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This paper considers robust consensus problem of a multi-agent systems under the communication constraints described by a communication graph. The uncertainty of each agent is modeled as a norm-bounded multiplicative uncertainty. A necessary and sufficient condition for achieving the robust consensus is characterized in terms of the eigenvalues of the weighted Laplacian of the communication graph. In the case where the nominal transfer function shared by all the agents is positive real, the robust consensus condition turns out to depend only on the largest eigenvalue. It is also shown that, if the nominal transfer function has a pole on the imaginary axis, the stability margin of the closed-loop multi-agent system is independent of the graph topology nor the number of the agents.