Robustness for Stability and Stabilization of Boolean Networks With Stochastic Function Perturbations

• 成果类型: Article
• 署名作者: Li, Haitao; Yang, Xinrong; Wang, Shuling
• 署名单位: Shandong Normal University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2997282
• 发表日期: 2021
• 页码: 1231-1237
• 关键词: Perturbation methods; Stochastic processes; Robustness; Stability criteria; BOOLEAN FUNCTIONS; genetics; Algebraic state space representation; Boolean network; robust stability; robust stabilization; stochastic function perturbations

摘要

In genetic regulatory networks (GRNs), gene mutations often occur in a stochastic manner. As an important model of GRNs, gene mutations of Boolean networks are always described as function perturbations. This article studies the robust stability and stabilization of Boolean networks with stochastic function perturbations. A kind of parameterized set is constructed, and it is revealed that under the stochastic function perturbations, the property of finite-time stability remains unchanged when the perturbed set and the parameterized set are disjoint. In addition, it is proved that the finite-time stability is reduced to stability in distribution when the intersection of perturbed set and complement set of parameterized set is nonempty. As an application, the robust stabilization problem of Boolean control networks with stochastic function perturbations is discussed, and several necessary and sufficient conditions are presented for the robustness of feedback stabilizers. Finally, the obtained results are used to study the Drosophila melanogaster segmentation polarity gene network and the lac operon in the bacterium Escherichia coil.