Stabilization and controller design of switched Boolean networks with minimum dwell time

Xinling Li; Shilin Wang; Xueying Nie; Tingmin Liu; Lei Deng; Xinling Li; Shilin Wang; Xueying Nie; Tingmin Liu; Lei Deng

doi:10.3934/math.20261127

AIMS Mathematics

2026, Volume 11, Issue 9: 28297-28317. doi: 10.3934/math.20261127

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Research article

Stabilization and controller design of switched Boolean networks with minimum dwell time

Research Center of Semi-tensor Product of Matrices: Theory and Applications, School of Mathematics and Systems Science, Liaocheng University, Liaocheng 252000, Shandong, China

Received: 31 May 2026 Revised: 19 August 2026 Accepted: 20 August 2026 Published: 04 September 2026
MSC : 93DXX; 93C05, 93D15, 93D23

This paper investigates the stabilization problem and the feedback controller design of switched Boolean control networks (SBCNs) consisting of two subnetworks, where minimum dwell time constraints are taken into consideration. First, the semi-tensor product method is utilized to convert the SBCNs with minimum dwell time constraints into an algebraic state-space model. Second, based on the relation between dwell time and the stabilization time of individual subsystems, some sufficient conditions are obtained to guarantee the global stabilization of the system, and feedback controllers which are dependent on system states and switching signals are designed. Finally, two practical examples are presented to validate the theoretical results of this paper.
- switched Boolean networks,
- minimum dwell time,
- stability,
- controller design,
- semi-tensor product
Citation: Xinling Li, Shilin Wang, Xueying Nie, Tingmin Liu, Lei Deng. Stabilization and controller design of switched Boolean networks with minimum dwell time[J]. AIMS Mathematics, 2026, 11(9): 28297-28317. doi: 10.3934/math.20261127

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Abstract

This paper investigates the stabilization problem and the feedback controller design of switched Boolean control networks (SBCNs) consisting of two subnetworks, where minimum dwell time constraints are taken into consideration. First, the semi-tensor product method is utilized to convert the SBCNs with minimum dwell time constraints into an algebraic state-space model. Second, based on the relation between dwell time and the stabilization time of individual subsystems, some sufficient conditions are obtained to guarantee the global stabilization of the system, and feedback controllers which are dependent on system states and switching signals are designed. Finally, two practical examples are presented to validate the theoretical results of this paper.

References

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