Finite-time stabilization of linear systems with time-varying delays using new integral inequalities

© 2019 by the Mathematical Association of Thailand. In this research we propose stability conditions for guaranteeing finite- time stabilization of linear systems with time-varying delay. Based on Lyapunov theory, improved finite-time stability and stabilization criteria of the linear systems are fo...

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Main Authors: Chantapish Zamart, Thaned Rojsiraphisal
Format: Journal
Published: 2019
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http://cmuir.cmu.ac.th/jspui/handle/6653943832/65680
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-656802019-08-05T04:39:23Z Finite-time stabilization of linear systems with time-varying delays using new integral inequalities Chantapish Zamart Thaned Rojsiraphisal Mathematics © 2019 by the Mathematical Association of Thailand. In this research we propose stability conditions for guaranteeing finite- time stabilization of linear systems with time-varying delay. Based on Lyapunov theory, improved finite-time stability and stabilization criteria of the linear systems are formulated in the form of linear matrix inequalities. To obtain the improved stability criteria, we first propose two new inequalities in the forms of free-matrix based inequality for bounding the integral of the form ∫t-d1t-d2 eα(t-s)x T (s)Rx(s)ds which is occurred in the derivative of Lyapunov-Krasovskii functional. By desiring a proper state-feedback controller, the non-linear terms occuring in the formula- tion can be managed without defining new variables. At the end, two numerical examples are given to show that the new criteria are praticable and can be applied to the case of continuous but not differentiable delay function. 2019-08-05T04:39:23Z 2019-08-05T04:39:23Z 2019-04-01 Journal 16860209 2-s2.0-85066809566 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85066809566&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/65680
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
Chantapish Zamart
Thaned Rojsiraphisal
Finite-time stabilization of linear systems with time-varying delays using new integral inequalities
description © 2019 by the Mathematical Association of Thailand. In this research we propose stability conditions for guaranteeing finite- time stabilization of linear systems with time-varying delay. Based on Lyapunov theory, improved finite-time stability and stabilization criteria of the linear systems are formulated in the form of linear matrix inequalities. To obtain the improved stability criteria, we first propose two new inequalities in the forms of free-matrix based inequality for bounding the integral of the form ∫t-d1t-d2 eα(t-s)x T (s)Rx(s)ds which is occurred in the derivative of Lyapunov-Krasovskii functional. By desiring a proper state-feedback controller, the non-linear terms occuring in the formula- tion can be managed without defining new variables. At the end, two numerical examples are given to show that the new criteria are praticable and can be applied to the case of continuous but not differentiable delay function.
format Journal
author Chantapish Zamart
Thaned Rojsiraphisal
author_facet Chantapish Zamart
Thaned Rojsiraphisal
author_sort Chantapish Zamart
title Finite-time stabilization of linear systems with time-varying delays using new integral inequalities
title_short Finite-time stabilization of linear systems with time-varying delays using new integral inequalities
title_full Finite-time stabilization of linear systems with time-varying delays using new integral inequalities
title_fullStr Finite-time stabilization of linear systems with time-varying delays using new integral inequalities
title_full_unstemmed Finite-time stabilization of linear systems with time-varying delays using new integral inequalities
title_sort finite-time stabilization of linear systems with time-varying delays using new integral inequalities
publishDate 2019
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85066809566&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/65680
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