Necessary and sufficient conditions for leader-following bipartite consensus with measurement noise

• Main Authors: Ma, Cui-Qin, Xie, Lihua
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2020
• Subjects: Engineering::Electrical and electronic engineering; Bipartite Consensus; Leader-following
• Online Access: https://hdl.handle.net/10356/139971
• Institution: Nanyang Technological University

This paper considers leader-following bipartite consensus of single-integrator multiagent systems in the presence of measurement noise. To attenuate the noise, a time-varying consensus gain q(t) is introduced into the stochastic approximation-type protocol. Necessary and sufficient conditions for ensuring a strong mean square leader-following bipartite consensus are given. In particular, in the absence of measurement noise, the convergence speed of error dynamics is dependent on the eigenvalues of Laplacian and the rate of ∫ 0 t q(s)ds approaching infinity. By appropriately choosing q(t), the speed of leader-following bipartite consensus convergence can be improved in a fixed communication topology. It is proven that conditions for the signed digraph to be structurally balanced and having a spanning tree are necessary and sufficient to ensure leader-following bipartite consensus, regardless of measurement noise.