Robustness is an important property for the analysis of network systems. In this article, we investigate the ability of probabilistic Boolean control networks (PBCNs) to keep output tracking to a constant reference signal under one-bit perturbation, and it is briefly termed as output robustness thereafter. Considering the output robustness of PBCNs, the traditional approaches in the preceding literature are disabled. To this end, we use the strongly connected components to characterize the invariant subset. The salient advantage of this approach is that the obtained invariant subset is equipped with a minute structure. Then, a component digraph is constructed. Based on it, two necessary and sufficient criteria are, respectively, derived for finite-time and asymptotic output tracking of PBCNs. Moreover, one-bit perturbation is classified into three categories with respect to different influence on the output tracking. Finally, a biological example demonstrates the availability of our theoretical results.

中文翻译：

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关于一位摄动的概率布尔控制网络的输出鲁棒性

健壮性是分析网络系统的重要属性。在本文中，我们研究了概率布尔控制网络（PBCN）在一位扰动下保持对恒定参考信号的输出跟踪的能力，此后简称为输出鲁棒性。考虑到PBCN的输出鲁棒性，禁用了先前文献中的传统方法。为此，我们使用强连接的组件来描述不变子集。该方法的显着优点是所获得的不变子集具有微小的结构。然后，构造分量图。在此基础上，分别导出了PBCN的有限时间和渐近输出跟踪的两个必要和充分标准。此外，相对于对输出跟踪的不同影响，一比特扰动可分为三类。最后，一个生物学的例子证明了我们理论结果的可用性。