Sampled-Data Based Mean Square Bipartite Consensus of Double-Integrator Multi-Agent Systems with Measurement Noises

  • Yifa Liu
  • Long ChengEmail author
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 528)


A distributed sampled-data based bipartite consensus protocol is proposed for double-integrator multi-agent systems with measurement noises under signed digraph. A time-varying consensus gain and the agents’ states feedback are adopted to counteract the noise effect and achieve bipartite consensus. By determining the state transition matrix of the multi-agent system, we describe the dynamic behaviour of the system. Under the proposed protocol, the states of some agents converge in mean square to one random vector while the rest of agents’ states are convergent to another random vector. It is noted that these two vector are at the same amplitude, however their signs are different. It is proved that sufficient conditions for achieving the mean square bipartite consensus are: (1) the topology graph is weighted balanced, structurally balanced and has a spanning tree; and (2) the time-varying consensus gain satisfies the stochastic approximation conditions. We verify the validity of the proposed protocol by numerical simulations.


Bipartite Consensus Multi-agent Systems (MASs) Measurement Noises Double-integrator Sampled-data 



This work was supported in part by the National Natural Science Foundation of China under Grant 61633016, in part by the Research Fund for Young Top-Notch Talent of National Ten Thousand Talent Program, and in part by the Beijing Municipal Natural Science Foundation under Grant 4162066.


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Management and Control for Complex SystemsInstitute of Automation, Chinese Academy of SciencesBeijingChina

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