Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable

Liang-jie SUN; Jian-quan LU; Wai-Ki CHING

doi:10.1631/FITEE.1900312

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Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable

Special Issue on Complex Systems and Networks with Their Applications | Updated：2022-05-19

- Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable
- 基于切换机制的所有子系统不稳定的非周期采样布尔控制网络镇定问题研究
- Frontiers of Information Technology & Electronic Engineering Vol. 21, Issue 2, Pages: 260-267(2020)
- Affiliations：
  
  School of Mathematics, Southeast University, Nanjing 210096, China
  Department of Mathematics, The University of Hong Kong, Hong Kong, China
- Author bio：
  
  [ "SUN Liang-jie,E-mail:1546258649@qq.com" ]
  [ "LU Jian-quan,E-mail:jqluma@seu.edu.cn" ]
  [ "CHING Wai-Ki,E-mail:wching@hku.hk" ]
- Funds：
- DOI：10.1631/FITEE.1900312
  CLC： TP183
- Received：24 June 2019，
  
  Revised：2019-10-23，
  
  Published Online：21 December 2019，
  
  Published：2020-02
- Accepted：
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Liang-jie SUN, Jian-quan LU, Wai-Ki CHING. Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 260-267.
DOI：

Liang-jie SUN, Jian-quan LU, Wai-Ki CHING. Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 260-267. DOI： 10.1631/FITEE.1900312.

摘要

本文旨在进一步研究带有非周期采样控制的布尔控制网络的全局稳定性。前期工作指出一个带有非周期采样控制的布尔控制网络能够被转化为一个切换布尔网络；通过研究转化后的切换布尔网络的全局稳定性，可以进一步得到带有非周期采样控制的布尔控制网络的全局稳定性。遗憾的是，由于前期工作主要思想是利用稳定子系统抵消由不稳定子系统引起的状态发散，因此所考虑的切换布尔网络至少含有一个稳定子系统。本文主旨是恰当的切换行为也可以具有良好稳定特性；即当所有子系统都不稳定时，通过设计合适的切换律，切换布尔网络也能达到稳定。这与前期工作的思想完全不同。具体地，对这种情况，首先驻留时间被要求限制在一对上下界内；然后，利用离散化李雅普诺夫函数和驻留时间方法，得到一个全局稳定的充分条件；最后，通过一个生物实例来论证所得结论。

Abstract

We aim to further study the global stability of Boolean control networks (BCNs) under aperiodic sampleddata control (ASDC). According to our previous work

it is known that a BCN under ASDC can be transformed into a switched Boolean network (SBN)

and further global stability of the BCN under ASDC can be obtained by studying the global stability of the transformed SBN. Unfortunately

since the major idea of our previous work is to use stable subsystems to offset the state divergence caused by unstable subsystems

the SBN considered has at least one stable subsystem. The central thought in this paper is that switching behavior also has good stabilization; i.e.

the SBN can also be stable with appropriate switching laws designed

even if all subsystems are unstable. This is completely different from that in our previous work. Specifically

for this case

the dwell time (DT) should be limited within a pair of upper and lower bounds. By means of the discretized Lyapunov function and DT

a sufficient condition for global stability is obtained. Finally

the above results are demonstrated by a biological example.

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