Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 58, Issue 4, Pages 935-946Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2012.2224251
Keywords
Consensus protocols; monotone systems; signed graphs; structural balance
Funding
- MIUR through a PRIN project at SISSA
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In a consensus protocol an agreement among agents is achieved thanks to the collaborative efforts of all agents, expresses by a communication graph with nonnegative weights. The question we ask in this paper is the following: is it possible to achieve a form of agreement also in presence of antagonistic interactions, modeled as negative weights on the communication graph? The answer to this question is affirmative: on signed networks all agents can converge to a consensus value which is the same for all agents except for the sign. Necessary and sufficient conditions are obtained to describe cases in which this is possible. These conditions have strong analogies with the theory of monotone systems. Linear and non-linear Laplacian feedback designs are proposed.
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