Necessary Stability Conditions for Linear Difference Equations in Continuous Time

A study on the stability of continuous-time difference equations is presented. Based on the construction of the analogous of the delay Lyapunov matrix for this class of equations, a complete type Lyapunov-Krasovskii functional is proposed, that allows to present necessary stability conditions. Examp...

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Vydané v:IEEE transactions on automatic control Ročník 63; číslo 12; s. 4405 - 4412
Hlavní autori: Campos, Emanuel Rocha, Mondie, Sabine, Di Loreto, Michael
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.12.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Predmet:
Automatic Control Engineering
Computer Science
Delays
Difference equations
Linear matrix inequalities
Linear theory
Lyapunov–Krasovskii
Mathematical analysis
Mathematical model
Stability
Stability criteria
Symmetric matrices
time-delay systems
time-delay systems
Lyapunov–Krasovskii
Linear theory
ISSN:0018-9286, 1558-2523
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Abstract A study on the stability of continuous-time difference equations is presented. Based on the construction of the analogous of the delay Lyapunov matrix for this class of equations, a complete type Lyapunov-Krasovskii functional is proposed, that allows to present necessary stability conditions. Examples are given throughout the paper to illustrate these conditions.
AbstractList A study on the stability of continuous-time difference equations is presented. Based on the construction of the analogous of the delay Lyapunov matrix for this class of equations, a complete type Lyapunov–Krasovskii functional is proposed, that allows to present necessary stability conditions. Examples are given throughout the paper to illustrate these conditions.
Author Di Loreto, Michael
Campos, Emanuel Rocha
Mondie, Sabine
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  givenname: Michael
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  surname: Di Loreto
  fullname: Di Loreto, Michael
  email: michael.di-loreto@insa-lyon.fr
  organization: Laboratoire Ampère CNRS UMR5005, National Institute of Applied Sciences of Lyon (INSA Lyon), University of Lyon, Villeurbanne, France
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Cites_doi 10.1016/j.automatica.2014.10.087
10.1007/978-0-8176-8367-2
10.1016/0022-247X(80)90289-9
10.1016/j.automatica.2014.10.031
10.1137/S0363012999355071
10.1016/j.sysconle.2013.06.003
10.1016/0024-3795(94)00183-9
10.1016/0022-247X(74)90149-8
10.1080/00207720903353625
10.1109/TAC.2003.815036
10.1109/TAC.2015.2437519
10.1002/rnc.2962
10.1137/080724940
10.1007/978-1-4612-4342-7
10.1016/S0167-6911(01)00114-1
10.1016/0022-247X(68)90038-3
10.1016/S0005-1098(02)00195-4
10.1016/j.automatica.2012.06.021
10.1016/S0005-1098(04)00243-2
10.1109/ICEEE.2011.6106678
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References ref13
ref12
ref15
ref14
ref20
ref11
ref10
ref21
ref1
ref17
damak (ref5) 2015
ref16
ref19
ref18
ref8
ref7
rocha (ref22) 0
ref9
ref4
ref3
ref6
hale (ref2) 1993
References_xml – ident: ref16
  doi: 10.1016/j.automatica.2014.10.087
– ident: ref1
  doi: 10.1007/978-0-8176-8367-2
– ident: ref8
  doi: 10.1016/0022-247X(80)90289-9
– ident: ref19
  doi: 10.1016/j.automatica.2014.10.031
– ident: ref9
  doi: 10.1137/S0363012999355071
– ident: ref4
  doi: 10.1016/j.sysconle.2013.06.003
– ident: ref13
  doi: 10.1016/0024-3795(94)00183-9
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  doi: 10.1016/0022-247X(74)90149-8
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  doi: 10.1080/00207720903353625
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  doi: 10.1109/TAC.2003.815036
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  doi: 10.1109/TAC.2015.2437519
– ident: ref21
  doi: 10.1002/rnc.2962
– ident: ref10
  doi: 10.1137/080724940
– year: 1993
  ident: ref2
  publication-title: Introduction to Functional Differential Equations
  doi: 10.1007/978-1-4612-4342-7
– ident: ref3
  doi: 10.1016/S0167-6911(01)00114-1
– year: 2015
  ident: ref5
  article-title: Approximation de systèmes à paramètres répartis : Analyse, simulation et commande
– ident: ref6
  doi: 10.1016/0022-247X(68)90038-3
– ident: ref18
  doi: 10.1016/S0005-1098(02)00195-4
– ident: ref11
  doi: 10.1016/j.automatica.2012.06.021
– start-page: 6507
  year: 0
  ident: ref22
  article-title: On the Lyapunov matrix of linear delay difference equations in continuous time
  publication-title: Proceedings of the 20th IFAC world congress
– ident: ref14
  doi: 10.1016/S0005-1098(04)00243-2
– ident: ref20
  doi: 10.1109/ICEEE.2011.6106678
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SubjectTerms Automatic Control Engineering
Computer Science
Delays
Difference equations
Linear matrix inequalities
Linear theory
Lyapunov–Krasovskii
Mathematical analysis
Mathematical model
Stability
Stability criteria
Symmetric matrices
time-delay systems
Title Necessary Stability Conditions for Linear Difference Equations in Continuous Time
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