Induced-Equations-Based Stability Analysis and Stabilization of Markovian Jump Boolean Networks

• 成果类型: Article
• 署名作者: Zhu, Shiyong; Lu, Jianquan; Lou, Yijun; Liu, Yang
• 署名单位: Southeast University - China; Chengdu University; Linyi University; Hong Kong Polytechnic University; Zhejiang Normal University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3037142
• 发表日期: 2021
• 页码: 4820-4827
• 关键词: Asymptotic stability; Stability criteria; switches; Perturbation methods; Mathematical model; Stochastic processes; Markov chain; Markovian jump Boolean networks; semitensor product of matrices; stability and stabilization; stochastic perturbation

摘要

This article considers asymptotic stability and stabilization of Markovian jump Boolean networks (MJBNs) with stochastic state-dependent perturbation. By defining an augmented random variable as the product of the canonical form of switching signal and state variable, asymptotic stability of an MJBN with perturbation is converted into the set stability of a Markov chain (MC). Then, the concept of induced equations is proposed for an MC, and the corresponding criterion is subsequently derived for asymptotic set stability of an MC by utilizing the solutions of induced equations. This criterion can be, respectively, examined by either a linear programming algorithm or a graphical algorithm. With regards to the stabilization of MJBNs, the time complexity is reduced to a certain extent. Furthermore, all time-optimal signal-based state feedback controllers are designed to stabilize an MJBN towards a given target state. Finally, the feasibility of the obtained results is demonstrated by two illustrative biological examples.