Robust Stability and Stabilisation of Delayed Boolean Networks With Disturbance

In this paper, we study a type of delayed Boolean networks(DBNs) which are affected by disturbances. We study the stability problems of this kind of DBNs based on algebraic form, which can be constructed by the semi-tensor product(STP) method. Firstly, the robust stability of DBNs without control is...

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Published inIEEE access Vol. 8; pp. 159471 - 159478
Main Authors Jiang, Chunfeng, Fu, Shihua, Zhao, Jianli
Format Journal Article
LanguageEnglish
Published Piscataway IEEE 2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Boolean
Boolean algebra
Boolean functions
Control stability
DBNs
Delay effects
disturbance inputs
Feedback control
Networks
Robust control
robust stabilisation
Robust stability
Robust stabilization
Robustness
Stability analysis
State feedback
STP
Tensors
Trajectory
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Abstract In this paper, we study a type of delayed Boolean networks(DBNs) which are affected by disturbances. We study the stability problems of this kind of DBNs based on algebraic form, which can be constructed by the semi-tensor product(STP) method. Firstly, the robust stability of DBNs without control is investigated, and the decision condition for robust stability is derived. Then, the robust stabilisation and control design problems are considered. Based on the algebraic representation of the delayed Boolean control networks(DBCNs), a necessary and sufficient condition is established to judge the robust stabilisation of the system, moreover, a state feedback control is also designed to robustly stabilize the DBCNs. Finally, we give an example to support our new results.
AbstractList In this paper, we study a type of delayed Boolean networks(DBNs) which are affected by disturbances. We study the stability problems of this kind of DBNs based on algebraic form, which can be constructed by the semi-tensor product(STP) method. Firstly, the robust stability of DBNs without control is investigated, and the decision condition for robust stability is derived. Then, the robust stabilisation and control design problems are considered. Based on the algebraic representation of the delayed Boolean control networks(DBCNs), a necessary and sufficient condition is established to judge the robust stabilisation of the system, moreover, a state feedback control is also designed to robustly stabilize the DBCNs. Finally, we give an example to support our new results.
Author Fu, Shihua
Zhao, Jianli
Jiang, Chunfeng
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10.1109/TAC.2013.2294821
10.1109/TNN.2011.2165556
10.1016/j.jfranklin.2018.09.004
10.1109/TCBB.2016.2555302
10.1016/j.automatica.2017.07.013
10.1016/j.automatica.2009.10.036
10.1002/asjc.2115
10.1016/j.neucom.2011.09.023
10.1016/j.amc.2012.06.071
10.1016/j.neucom.2007.03.011
10.1016/0022-5193(69)90015-0
10.1016/j.automatica.2009.03.006
10.1016/j.automatica.2011.01.040
10.1016/j.neucom.2018.10.005
10.1002/asjc.2126
10.1007/s11704-014-3425-y
10.1016/j.automatica.2012.03.024
10.1371/journal.pone.0042095
10.1155/2018/1737685
10.1137/140991820
10.1109/TNN.2011.2126594
10.1109/JAS.2016.7510259
10.1137/18M1170443
10.1016/j.jfranklin.2017.09.024
10.1049/iet-cta.2017.0014
10.1080/00207721.2016.1212433
10.1007/s11427-017-9265-8
10.1016/j.automatica.2016.01.075
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References ref13
ref12
ref15
ref14
ref31
ref30
ref11
ref10
ref17
ref16
kauffman (ref1) 1969; 22
ref18
li (ref22) 2011; 22
wu (ref19) 2011; 22
ref24
ref26
ref25
ref20
ref21
ref28
ref27
ref29
ref8
liu (ref23) 2018; 29
ref7
ref9
ref4
ref3
ref6
ref5
cheng (ref2) 2011
References_xml – ident: ref3
  doi: 10.1142/8323
– ident: ref7
  doi: 10.1109/TAC.2013.2294821
– volume: 22
  start-page: 1685
  year: 2011
  ident: ref19
  article-title: Delay-independent stability of genetic regulatory networks
  publication-title: IEEE Trans Neural Netw
  doi: 10.1109/TNN.2011.2165556
– ident: ref8
  doi: 10.1016/j.jfranklin.2018.09.004
– ident: ref30
  doi: 10.1109/TCBB.2016.2555302
– ident: ref29
  doi: 10.1016/j.automatica.2017.07.013
– ident: ref6
  doi: 10.1016/j.automatica.2009.10.036
– ident: ref9
  doi: 10.1002/asjc.2115
– ident: ref26
  doi: 10.1016/j.neucom.2011.09.023
– ident: ref24
  doi: 10.1016/j.amc.2012.06.071
– ident: ref25
  doi: 10.1016/j.neucom.2007.03.011
– volume: 22
  start-page: 437
  year: 1969
  ident: ref1
  article-title: Metabolic stability and epigenesis in randomly constructed genetic nets
  publication-title: J Theor Biol
  doi: 10.1016/0022-5193(69)90015-0
– ident: ref5
  doi: 10.1016/j.automatica.2009.03.006
– volume: 29
  start-page: 3283
  year: 2018
  ident: ref23
  article-title: Delayed feedback control for stabilization of Boolean control networks with state delay
  publication-title: IEEE Trans Neural Netw Learn Syst
– ident: ref21
  doi: 10.1016/j.automatica.2011.01.040
– ident: ref18
  doi: 10.1016/j.neucom.2018.10.005
– ident: ref13
  doi: 10.1002/asjc.2126
– ident: ref16
  doi: 10.1007/s11704-014-3425-y
– ident: ref14
  doi: 10.1016/j.automatica.2012.03.024
– ident: ref17
  doi: 10.1371/journal.pone.0042095
– ident: ref31
  doi: 10.1155/2018/1737685
– ident: ref10
  doi: 10.1137/140991820
– year: 2011
  ident: ref2
  publication-title: Analysis and Control of Boolean Networks A Semi-Tensor Product Approach
– volume: 22
  start-page: 948
  year: 2011
  ident: ref22
  article-title: Observability of Boolean control networks with state time delays
  publication-title: IEEE Trans Neural Netw
  doi: 10.1109/TNN.2011.2126594
– ident: ref12
  doi: 10.1109/JAS.2016.7510259
– ident: ref4
  doi: 10.1137/18M1170443
– ident: ref20
  doi: 10.1016/j.jfranklin.2017.09.024
– ident: ref11
  doi: 10.1049/iet-cta.2017.0014
– ident: ref27
  doi: 10.1080/00207721.2016.1212433
– ident: ref15
  doi: 10.1007/s11427-017-9265-8
– ident: ref28
  doi: 10.1016/j.automatica.2016.01.075
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StartPage 159471
SubjectTerms Boolean
Boolean algebra
Boolean functions
Control stability
DBNs
Delay effects
disturbance inputs
Feedback control
Networks
Robust control
robust stabilisation
Robust stability
Robust stabilization
Robustness
Stability analysis
State feedback
STP
Tensors
Trajectory
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Title Robust Stability and Stabilisation of Delayed Boolean Networks With Disturbance
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