Perturbation Analysis for Finite-Time Stability and Stabilization of Probabilistic Boolean Networks

This article analyzes the function perturbation impact on the finite-time stability and stabilization of the probabilistic Boolean networks (PBNs). First, the concept of stability in the distribution of PBNs is divided into two disjoint concepts, that is, finite-time stability with probability one (...

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Bibliographic Details
Published in:IEEE transactions on cybernetics Vol. 51; no. 9; pp. 4623 - 4633
Main Authors: Li, Haitao, Yang, Xinrong, Wang, Shuling
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.09.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algebraic state-space representation (ASSR)
Asymptotic stability
Boolean
Boolean algebra
Boolean functions
Control stability
E coli
finite-time stability
function perturbation
Networks
Nonlinear systems
Parameterization
Perturbation methods
probabilistic Boolean network (PBN)
Probabilistic logic
Stability analysis
Stability criteria
stabilization
Statistical analysis
Stochastic systems
ISSN:2168-2267, 2168-2275, 2168-2275
Online Access:Get full text
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Summary:This article analyzes the function perturbation impact on the finite-time stability and stabilization of the probabilistic Boolean networks (PBNs). First, the concept of stability in the distribution of PBNs is divided into two disjoint concepts, that is, finite-time stability with probability one (FTSPO) and asymptotical stability with probability one (ASPO), and a new criterion is proposed for the verification of ASPO. Second, by constructing a parameterized set, it is shown that PBNs subject to function perturbation keep FTSPO if and only if the perturbed point does not belong to the parameterized set, while PBNs become ASPO if and only if the perturbed point belongs to the parameterized set. Third, as an application of perturbed stability analysis, the robust state-feedback stabilization is discussed for probabilistic Boolean control networks (PBCNs) with function perturbation. Finally, the obtained results are applied to a WNT5A network and lac operon in the Escherichia coli , respectively.
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2020.3003055