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Bipartite Linear χ ‐Consensus of Double‐Integrator Multi‐Agent Systems With Measurement Noise
Author(s) -
Ma Cuiqin,
Zhao Weiwei,
Zhao YunBo
Publication year - 2018
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1546
Subject(s) - bipartite graph , algebraic graph theory , digraph , mathematics , consensus , signed graph , multi agent system , protocol (science) , state (computer science) , algebraic number , discrete mathematics , graph , computer science , combinatorics , algorithm , artificial intelligence , medicine , mathematical analysis , alternative medicine , pathology
Abstract The bipartite consensus problem is investigated for double‐integrator multi‐agent systems in the presence of measurement noise. A distributed protocol with time‐varying consensus gain is proposed. By using tools of state transition matrix and algebraic graph theory, necessary and sufficient conditions for the designed protocol to be a mean square bipartite linear χ ‐consensus protocol are given. It is shown that the signed digraph being structurally balanced and having a spanning tree are not only sufficient, but also necessary for bipartite consensus. Furthermore, the protocol is proved to be a mean square bipartite average consensus protocol if the signed graph is weight balanced.