Allowable delay bound for consensus of linear multi-agent systems with communication delay

Ya Zhang and Yu-Ping Tian

International Journal of Systems Science, 2014, vol. 45, issue 10, 2172-2181

Abstract: This paper studies the consensus of a group of linear dynamic agents with a uniform communication delay and focuses on searching an allowable delay bound. As long as the delay is less than this bound, there exist linear feedback consensus protocols driving the multi-agent system to achieve consensus. Both fixed and switching topology cases are investigated. In both cases, the consensus problem is converted to the robust stability problem of corresponding uncertain state-delayed systems. By using Lyapunov–Krasovskii functional analysis, consensus conditions which contain the feedback gain conditions and delay conditions are proposed for systems over fixed and switching topologies, respectively. Furthermore, allowable delay bounds are obtained for both systems by solving the optimal robust stabilisation problems. Numerical examples are given to illustrate the results.

Date: 2014
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DOI: 10.1080/00207721.2013.763303

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