An input-output approach to H∞ reduced filter design for polytopic time-varying delay systems

This paper discusses the problem of delay-dependent robust filtering design for polytopic systems with a time-varying delay. A new model transformation is firstly applied by employing a three-term approximation for the delayed state, which leads to a smaller approximation error than the two-term app...

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Published in:	International journal of systems science Vol. 50; no. 1; pp. 35 - 49
Main Authors:	El Aiss, Hicham, Zoulagh, Taha, Hmamed, Abdelaziz, El Hajjaji, Ahmed
Format:	Journal Article
Language:	English
Published:	London Taylor & Francis 02.01.2019 Taylor & Francis Ltd
Subjects:	Approximation Automatic Delay-dependent criteria Design engineering Electric power Engineering Sciences Error analysis filter Filter design (mathematics) Filtration Linear matrix inequalities linear matrix inequality (LMI) Linearization Mathematical analysis Matrix methods polytopic uncertainties Reduced order filters Time delay systems time-varying delay
ISSN:	0020-7721, 1464-5319
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Abstract	This paper discusses the problem of delay-dependent robust filtering design for polytopic systems with a time-varying delay. A new model transformation is firstly applied by employing a three-term approximation for the delayed state, which leads to a smaller approximation error than the two-term approximation. Then, based on the scaled small-gain Theorem combined with an appropriate Lyapunov-Krasovskii Functional, the performance analysis of the filtering error system is examined and then the full- and reduced-order filters are designed in terms of linear matrix inequalities via a simple linearisation technique. Before the end, a sufficient condition is presented to solve the problem of filtering design for a time-delay system without polytopic uncertainties. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods.
AbstractList	This paper discusses the problem of delay-dependent robust filtering design for polytopic systems with a time-varying delay. A new model transformation is firstly applied by employing a three-term approximation for the delayed state, which leads to a smaller approximation error than the two-term approximation. Then, based on the scaled small-gain Theorem combined with an appropriate Lyapunov-Krasovskii Functional, the performance analysis of the filtering error system is examined and then the full- and reduced-order filters are designed in terms of linear matrix inequalities via a simple linearisation technique. Before the end, a sufficient condition is presented to solve the problem of filtering design for a time-delay system without polytopic uncertainties. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods. This paper discusses the problem of delay-dependent robust [Formula omitted.] filtering design for polytopic systems with a time-varying delay. A new model transformation is firstly applied by employing a three-term approximation for the delayed state, which leads to a smaller approximation error than the two-term approximation. Then, based on the scaled small-gain Theorem combined with an appropriate Lyapunov-Krasovskii Functional, the [Formula omitted.] performance analysis of the filtering error system is examined and then the [Formula omitted.] full- and reduced-order filters are designed in terms of linear matrix inequalities via a simple linearisation technique. Before the end, a sufficient condition is presented to solve the problem of [Formula omitted.] filtering design for a time-delay system without polytopic uncertainties. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods.
Author	El Aiss, Hicham Hmamed, Abdelaziz El Hajjaji, Ahmed Zoulagh, Taha
Author_xml	– sequence: 1 givenname: Hicham surname: El Aiss fullname: El Aiss, Hicham email: elaiss.hicham@gmail.com organization: Department of Physics, Faculty of Sciences Dhar El Mahraz-Fes, University of Sidi Mohamed Ben Abdellah – sequence: 2 givenname: Taha orcidid: 0000-0003-4796-2744 surname: Zoulagh fullname: Zoulagh, Taha organization: Department of Physics, Faculty of Sciences Dhar El Mahraz-Fes, University of Sidi Mohamed Ben Abdellah – sequence: 3 givenname: Abdelaziz surname: Hmamed fullname: Hmamed, Abdelaziz organization: Department of Physics, Faculty of Sciences Dhar El Mahraz-Fes, University of Sidi Mohamed Ben Abdellah – sequence: 4 givenname: Ahmed surname: El Hajjaji fullname: El Hajjaji, Ahmed organization: MIS Lab. UFR of Sciences, University of Picardie Jules Vene
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Snippet	This paper discusses the problem of delay-dependent robust filtering design for polytopic systems with a time-varying delay. A new model transformation is... This paper discusses the problem of delay-dependent robust [Formula omitted.] filtering design for polytopic systems with a time-varying delay. A new model...
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SubjectTerms	Approximation Automatic Delay-dependent criteria Design engineering Electric power Engineering Sciences Error analysis filter Filter design (mathematics) Filtration Linear matrix inequalities linear matrix inequality (LMI) Linearization Mathematical analysis Matrix methods polytopic uncertainties Reduced order filters Time delay systems time-varying delay
Title	An input-output approach to H∞ reduced filter design for polytopic time-varying delay systems
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