Consensus of discrete-time multi-agent systems with unbounded time-varying delays
作者单位：School of Automation Southeast University School of Automation Hangzhou Dianzi University
会议名称：《第三十九届中国控制会议》
会议日期：2020年
学科分类：0711[理学-系统科学] 07[理学] 08[工学] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 071102[理学-系统分析与集成] 081103[工学-系统工程]
关 键 词：Time-delay system Consensus Discrete-time system Unbounded time-delay Infinite maximum delay
摘 要：This paper studies the modeling and convergence of discrete-time distributed consensus algorithms with unbounded time-varying delays. Firstly, we reveal that when the consensus algorithm with unbounded time-varying delays is modeled as a time-delay system, the maximum delay in the system equation increases to infinity as time goes on. While this property prevents us from using most tools for convergence analysis of conventional discrete time-delay systems, we study the properties of the system state by building a finite dimensional delay system model in the interval [0, k] for any finite positive integer k. Next, we prove that, under the assumption that the growth rate of the maximum delay is slower than the growth rate of a K∞ class function,and the system topology contains a spanning tree, the consensus algorithm with unbounded time-varying delays can achieve a consensus. And the convergence rate of the algorithm is also characterized. Finally, the simulation experiment demonstrates the correctness of the theoretic result of the paper.