On robust set stability and set stabilization of probabilistic Boolean control networks

Jianjun Wang, Wen Liu, Shihua Fu and Jianwei Xia

Applied Mathematics and Computation, 2022, vol. 422, issue C

Abstract: Under the semi-tensor product method, this paper investigates the robust set stability and robust set stabilization problems for a class of probabilistic Boolean control networks (PBCNs) with disturbances. First, an algorithm to determine the largest robust invariant set (LRIS) of a given set for a PBN with probability one is proposed, and the necessary and sufficient conditions to detect whether the PBN is globally finite-time stable to this invariant set with probability one are established. Second, the PBNs with control inputs are considered, and an algorithm for the largest robust control invariant set (LRCIS) with probability one is provided, based on which, some necessary and sufficient conditions for finite-time robust set stabilization with probability one of PBCNs are presented. Furthermore, the design scheme of time-optimal state feedback stabilizers via antecedence solution technique is derived. The study of illustrative examples shows the effectiveness of the obtained new results.

Keywords: Probabilistic Boolean control networks; The largest robust invariant set; Robust set stability; Robust set stabilization; Semi-tensor product of matrices (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:422:y:2022:i:c:s0096300322000789

DOI: 10.1016/j.amc.2022.126992

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