Asymptotical stability and stabilisation of probabilistic Boolean networks subject to function perturbation

• Published in: International journal of control Vol. 95; no. 11; pp. 3118 - 3126
• Main Authors: Yang, Xinrong, Li, Haitao
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.11.2022; Taylor & Francis Ltd
• Subjects: algebraic state space representation; Asymptotic properties; asymptotical stabilisation; asymptotical stability; Boolean functions; function perturbation; Mathematical analysis; Networks; Perturbation; Probabilistic Boolean network; Probability theory; Stability criteria; Statistical analysis
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2021.1955977

This paper focuses on the effects of function perturbation for probabilistic Boolean networks (PBNs), including asymptotical stability and stabilisation. Firstly, by constructing a proper set, a necessary and sufficient condition is presented for the asymptotically stable PBN being stable in distribution after function perturbation. Secondly, by removing the case of changing to finite-time stability with probability one from the case of changing to stability in distribution, some criteria are given for the asymptotically stable PBN keeping asymptotically stable after function perturbation. These criteria need to calculate the number of positive-probability cycles. In order to simplify the calculation, two sufficient conditions are further established. Finally, as an application, the robustness of asymptotical feedback stabilisers is further studied for probabilistic Boolean control networks subject to function perturbation.