New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique

New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique

A novel combined convex method is developed for the stability of linear systems with a time-varying delay. A new delay-dependent stability condition expressed in terms of linear matrix inequalities (LMIs) is derived by employing a dedicated constructed Lyapunov-Krasovskii functional (LKF), utilizing...

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Main Authors: Bin Yang, Chen-xin Fan
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2015/425864
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spelling doaj-ad7048e1f45a45278060f1e53f4ceaa02020-11-24T22:08:01ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/425864425864New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex TechniqueBin Yang0Chen-xin Fan1The School of Control Science and Engineering, Dalian University of Technology, Dalian 116023, ChinaThe School of Control Science and Engineering, Dalian University of Technology, Dalian 116023, ChinaA novel combined convex method is developed for the stability of linear systems with a time-varying delay. A new delay-dependent stability condition expressed in terms of linear matrix inequalities (LMIs) is derived by employing a dedicated constructed Lyapunov-Krasovskii functional (LKF), utilizing the Wirtinger inequality and the reciprocally convex approach to handle the integral term of quadratic quantities. Different from the previous convex techniques which only tackle the time-varying delay, our method adopts the idea of combined convex technique which can tackle not only the delay but also the delay variation. Four well-known examples are illustrated to show the effectiveness of the proposed results.http://dx.doi.org/10.1155/2015/425864
collection DOAJ
language English
format Article
sources DOAJ
author Bin Yang
Chen-xin Fan
spellingShingle Bin Yang
Chen-xin Fan
New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique
Mathematical Problems in Engineering
author_facet Bin Yang
Chen-xin Fan
author_sort Bin Yang
title New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique
title_short New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique
title_full New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique
title_fullStr New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique
title_full_unstemmed New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique
title_sort new stability analysis for linear systems with time-varying delay based on combined convex technique
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2015-01-01
description A novel combined convex method is developed for the stability of linear systems with a time-varying delay. A new delay-dependent stability condition expressed in terms of linear matrix inequalities (LMIs) is derived by employing a dedicated constructed Lyapunov-Krasovskii functional (LKF), utilizing the Wirtinger inequality and the reciprocally convex approach to handle the integral term of quadratic quantities. Different from the previous convex techniques which only tackle the time-varying delay, our method adopts the idea of combined convex technique which can tackle not only the delay but also the delay variation. Four well-known examples are illustrated to show the effectiveness of the proposed results.
url http://dx.doi.org/10.1155/2015/425864
work_keys_str_mv AT binyang newstabilityanalysisforlinearsystemswithtimevaryingdelaybasedoncombinedconvextechnique
AT chenxinfan newstabilityanalysisforlinearsystemswithtimevaryingdelaybasedoncombinedconvextechnique
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