离散时间分数阶多自主体系统的时延一致性

复杂工作环境中，许多自然现象的个体动力学特性用整数阶方程不能描述，只能用非整数阶（分数阶）动力学来描述个体的运动行为. 本文假设多自主体系统内部连接组成有向加权网络，个体的动态特性应用分数阶动力学方程描述，个体之间数据传输存在通信时延. 应用分数阶系统的Laplace变换和频域理论，研究了离散时间的分数阶多自主体系统的渐近一致性. 应用Hermit-Biehler 定理，研究了具有样本时延的分数阶多自主体系统的运动一致性，得到保证系统稳定的时延的上界阈值. 最后应用一个实例对结论进行了验证.

Delay Consensus of Fractional-order Multi-agent Systems with Sampling Delays

In the complex practical environments, many distributed multi-agent systems can not be described with the integer-order dynamics and can only be illustrated with the fractional-order dynamics. In this paper, consensus problems of discrete-time networked fractional-order multi-agent systems with sampling delay are investigated. Firstly, the collaborative control of discrete-time multi-agent systems with fractional-order operator is analyzed in a directed network ignoring sampling delay by using Laplace transform and frequency domain. Then, by applying Hermit-Biehler theorem, the consensus of fractional-order multi-agent systems with sampling delay is studied in a misdirected network. A number of consensus conditions for fractional-order systems with sampling delay are obtained. Numerical simulations are shown to illustrate the utility of the theoretical results.