Finite-Time Stability and H∞ Control of Linear Discrete-Time Delay Systems with Norm-Bounded Disturbances

This paper deals with the finite-time stability and H ∞ control of linear discrete-time delay systems. The system under consideration is subject to interval time-varying delay and norm-bounded disturbances. Linear matrix inequality approach is used to solve the finite-time stability problem. First,...

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Published inActa mathematica vietnamica Vol. 41; no. 3; pp. 481 - 493
Main Authors Tuan, Le A., Phat, Vu N.
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.09.2016
Subjects
Mathematics
Mathematics and Statistics
Finite-time stability
Time-varying delay
34D10
Disturbances
49M7
control
Linear matrix inequalities
34K20
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ISSN0251-4184
2315-4144
DOI10.1007/s40306-015-0155-7

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Abstract This paper deals with the finite-time stability and H ∞ control of linear discrete-time delay systems. The system under consideration is subject to interval time-varying delay and norm-bounded disturbances. Linear matrix inequality approach is used to solve the finite-time stability problem. First, new sufficient conditions are established for robust finite-time stability of the linear discrete-time delay system with norm-bounded disturbances, then the state feedback controller is designed to robustly finite-time stabilize the system and guarantee an adequate level of system performance. The delay-dependent sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed results.
AbstractList This paper deals with the finite-time stability and H ∞ control of linear discrete-time delay systems. The system under consideration is subject to interval time-varying delay and norm-bounded disturbances. Linear matrix inequality approach is used to solve the finite-time stability problem. First, new sufficient conditions are established for robust finite-time stability of the linear discrete-time delay system with norm-bounded disturbances, then the state feedback controller is designed to robustly finite-time stabilize the system and guarantee an adequate level of system performance. The delay-dependent sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed results.
Author Phat, Vu N.
Tuan, Le A.
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Cites_doi 10.1016/j.jfranklin.2014.03.010
10.1007/s11063-012-9243-z
10.1080/00207720701832531
10.1016/j.cnsns.2008.03.010
10.1016/j.jfranklin.2010.12.001
10.1016/j.jfranklin.2013.06.017
10.1007/s11768-011-8213-8
10.1016/j.jfranklin.2014.02.008
10.1016/j.automatica.2010.02.008
10.1016/j.cnsns.2012.05.002
10.1016/j.amc.2011.11.057
10.1137/1.9781611970777
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Keywords Finite-time stability
Time-varying delay
34D10
Disturbances
49M7
control
Linear matrix inequalities
34K20
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References Zhang, Liu, Mu (CR14) 2012; 218
CR2
Meng, Shen (CR7) 2009; 14
CR4
CR3
Liu, Zhang, He, Zhang (CR6) 2011; 9
He, Wu, Han, She (CR5) 2008; 39
CR12
Stojanovic, Debeljkovic, Antic (CR9) 2014; 351
Amato, Ariola, Cosentino (CR1) 2010; 46
Song, Yu, Zhang, Zhang (CR8) 2012; 17
Xiang (CR11) 2011; 348
Zhang, Zhang, Zheng, Kamiri (CR13) 2014; 351
Tuan, Nam, Phat (CR10) 2013; 37
Zuo, Li, Wang (CR15) 2013; 350
W Xiang (155_CR11) 2011; 348
Q Meng (155_CR7) 2009; 14
Y He (155_CR5) 2008; 39
F Amato (155_CR1) 2010; 46
H Song (155_CR8) 2012; 17
Z Zhang (155_CR13) 2014; 351
155_CR2
LA Tuan (155_CR10) 2013; 37
155_CR4
155_CR3
155_CR12
J Liu (155_CR6) 2011; 9
Z Zuo (155_CR15) 2013; 350
Y Zhang (155_CR14) 2012; 218
SB Stojanovic (155_CR9) 2014; 351
References_xml – volume: 351
  start-page: 3914
  year: 2014
  end-page: 3931
  ident: CR9
  article-title: The application of different Lyapunov-like functionals and some aggregate norm approximations of the delayed states for finite-time stability analysis of linear discrete time-delay systems
  publication-title: J. Franklin Inst
  doi: 10.1016/j.jfranklin.2014.03.010
– ident: CR3
– ident: CR4
– ident: CR2
– volume: 37
  start-page: 235
  year: 2013
  end-page: 249
  ident: CR10
  article-title: New controller design for neural networks with interval time-varying delays in state and observation
  publication-title: Neural. Process Lett.
  doi: 10.1007/s11063-012-9243-z
– volume: 39
  start-page: 427
  year: 2008
  end-page: 436
  ident: CR5
  article-title: Delay-dependent control of linear discrete-time systems with an interval-like time-varying delay
  publication-title: Int. J. Syst. Sci.
  doi: 10.1080/00207720701832531
– ident: CR12
– volume: 14
  start-page: 1043
  year: 2009
  end-page: 1049
  ident: CR7
  article-title: Finite-time control for linear continuous system with norm-bounded disturbance
  publication-title: Commun. Nonlinear Sci. Numer. Simul
  doi: 10.1016/j.cnsns.2008.03.010
– volume: 348
  start-page: 331
  year: 2011
  end-page: 352
  ident: CR11
  article-title: Xiao, J.: finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance
  publication-title: J. Franklin Inst
  doi: 10.1016/j.jfranklin.2010.12.001
– volume: 350
  start-page: 2745
  year: 2013
  end-page: 2756
  ident: CR15
  article-title: New criterion for finite-time stability of linear discrete-time systems with time-varying delay
  publication-title: J. Franklin Inst.
  doi: 10.1016/j.jfranklin.2013.06.017
– volume: 9
  start-page: 611
  year: 2011
  end-page: 616
  ident: CR6
  article-title: New results on robust control for discrete-time systems with interval time-varying delays
  publication-title: J. Control Theory Appl
  doi: 10.1007/s11768-011-8213-8
– volume: 351
  start-page: 3457
  year: 2014
  end-page: 3476
  ident: CR13
  article-title: Finite-time stability analysis and stabilization for linear discrete-time system with time-varying delay
  publication-title: J. Franklin Inst.
  doi: 10.1016/j.jfranklin.2014.02.008
– volume: 46
  start-page: 919
  year: 2010
  end-page: 924
  ident: CR1
  article-title: Finite-time control of discrete-time linear systems: analysis and design conditions
  publication-title: Automatica
  doi: 10.1016/j.automatica.2010.02.008
– volume: 17
  start-page: 4802
  year: 2012
  end-page: 4814
  ident: CR8
  article-title: Finite-time control for a class of discrete-time switched time-delay systems with quantized feedback
  publication-title: Commun. Nonlinear Sci. Numer. Simul
  doi: 10.1016/j.cnsns.2012.05.002
– volume: 218
  start-page: 5629
  year: 2012
  end-page: 5640
  ident: CR14
  article-title: Robust finite-time control of singular stochastic systems via static output feedback
  publication-title: Appl. Math. Comput.
– volume: 46
  start-page: 919
  year: 2010
  ident: 155_CR1
  publication-title: Automatica
  doi: 10.1016/j.automatica.2010.02.008
– volume: 9
  start-page: 611
  year: 2011
  ident: 155_CR6
  publication-title: J. Control Theory Appl
  doi: 10.1007/s11768-011-8213-8
– volume: 37
  start-page: 235
  year: 2013
  ident: 155_CR10
  publication-title: Neural. Process Lett.
  doi: 10.1007/s11063-012-9243-z
– volume: 17
  start-page: 4802
  year: 2012
  ident: 155_CR8
  publication-title: Commun. Nonlinear Sci. Numer. Simul
  doi: 10.1016/j.cnsns.2012.05.002
– ident: 155_CR3
– ident: 155_CR4
– volume: 218
  start-page: 5629
  year: 2012
  ident: 155_CR14
  publication-title: Appl. Math. Comput.
  doi: 10.1016/j.amc.2011.11.057
– volume: 14
  start-page: 1043
  year: 2009
  ident: 155_CR7
  publication-title: Commun. Nonlinear Sci. Numer. Simul
  doi: 10.1016/j.cnsns.2008.03.010
– volume: 348
  start-page: 331
  year: 2011
  ident: 155_CR11
  publication-title: J. Franklin Inst
  doi: 10.1016/j.jfranklin.2010.12.001
– ident: 155_CR12
– volume: 39
  start-page: 427
  year: 2008
  ident: 155_CR5
  publication-title: Int. J. Syst. Sci.
  doi: 10.1080/00207720701832531
– volume: 350
  start-page: 2745
  year: 2013
  ident: 155_CR15
  publication-title: J. Franklin Inst.
  doi: 10.1016/j.jfranklin.2013.06.017
– volume: 351
  start-page: 3457
  year: 2014
  ident: 155_CR13
  publication-title: J. Franklin Inst.
  doi: 10.1016/j.jfranklin.2014.02.008
– ident: 155_CR2
  doi: 10.1137/1.9781611970777
– volume: 351
  start-page: 3914
  year: 2014
  ident: 155_CR9
  publication-title: J. Franklin Inst
  doi: 10.1016/j.jfranklin.2014.03.010
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Title Finite-Time Stability and H∞ Control of Linear Discrete-Time Delay Systems with Norm-Bounded Disturbances
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