Output Robustness of Probabilistic Boolean Control Networks With Respect to One-Bit Perturbation

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.