论文标题
相应分数网络的稳定性和鲁棒性分析
Stability and Robustness Analysis of Commensurate Fractional-order Networks
论文作者
论文摘要
由生化反应网络激励，提供了经典割线条件的概括，用于循环互连的相称分数系统的稳定性分析。当描述网络符合单个电路时，主要的结果表明了分数订单系统的循环互连网络稳定性的足够条件。在耦合权重均匀的特殊情况下，条件变得必要。然后，我们研究了分数线性网络的鲁棒性。使用动态系统的$ \ MATHCAL {H} _2 $ -NORM来量化分数线性网络的鲁棒性能。最后，理论结果通过一些数值插图确认。
Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected commensurate fractional-order systems is provided. The main result presents a sufficient condition for stability of networks of cyclic interconnection of fractional-order systems when the digraph describing the network conforms to a single circuit. The condition becomes necessary under a special situation where coupling weights are uniform. We then investigate the robustness of fractional-order linear networks. Robustness performance of a fractional-order linear network is quantified using the $\mathcal{H}_2$-norm of the dynamical system. Finally, the theoretical results are confirmed via some numerical illustrations.
