针对具有双向等时延的二阶无向通信拓扑系统,采用带有通信时滞的线性一致控制率协议,分析了使系统稳定的条件.由于系统的阶次较高,直接对其特征方程进行分析是比较困难的,提出了一种新的分析方法,把系统的特征方程分解为多个子系统的乘积,然后利用CTCR方法,求得每个子系统对应的时滞最大值,比较后得出使系统达到一致稳定的最大时滞,作出了控制率边界曲线图并标出了稳定区域.结果表明,在有向生成树的情况下,当时滞小于决策值时,系统能达到稳定.最后,数值仿真验证了所得结果的有效性.%For a class of second-order multi-agent systems with a fixed and undirected communication topology and uniform delays systems, linear consensus protocols with time-delayed communications are adopted, the stability conditions are analysised. As the order of system is very high, the stability analysis of the characteristic equation becomes intractable. This paper proposes a new analysis approach via decomposing the characteristic equation of system into a set of factors and using the CTCR method, derives the communication delay of each eigenvalue, and obtains the accurate upper bound of delay of the system. We also explore the stability region generated through the protocol. The results show that in a case of a spanning tree, when time delay is less than the decision value, the stability of the system can be achieved. Finally, numerical simulation shows the effectiveness of the results.
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