Refined Jensen-based inequality approach to stability analysis of time-delay systems

In this study, the authors derive some new refined Jensen-based inequalities, which encompass both the Jensen inequality and its most recent improvement based on the Wirtinger integral inequality. The potential capability of this approach is demonstrated through applications to stability analysis of...

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Vydané v:	IET control theory & applications Ročník 9; číslo 14; s. 2188 - 2194
Hlavní autori:	Hien, Le Van, Trinh, Hieu
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	The Institution of Engineering and Technology 17.09.2015
Predmet:	Algorithms Brief Papers Constants convex optimisation algorithms convex programming Criteria Delay delays discrete distributed constant delays systems Inequalities interval time‐varying delay systems linear matrix inequalities Optimization refined Jensen‐based inequality approach Stability Stability analysis stability criteria time‐varying systems Wirtinger integral inequality Wirtinger integral inequality time-varying systems linear matrix inequalities delays stability analysis refined Jensen-based inequality approach discrete distributed constant delays systems stability criteria convex programming interval time-varying delay systems convex optimisation algorithms
ISSN:	1751-8644, 1751-8652
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Abstract	In this study, the authors derive some new refined Jensen-based inequalities, which encompass both the Jensen inequality and its most recent improvement based on the Wirtinger integral inequality. The potential capability of this approach is demonstrated through applications to stability analysis of time-delay systems. More precisely, by using the newly derived inequalities, they establish new stability criteria for two classes of time-delay systems, namely discrete and distributed constant delays systems and interval time-varying delay systems. The resulting stability conditions are derived in terms of linear matrix inequalities, which can be efficiently solved by various convex optimisation algorithms. Numerical examples are given to show the effectiveness and least conservativeness of the results obtained in this study.
AbstractList	In this study, the authors derive some new refined Jensen‐based inequalities, which encompass both the Jensen inequality and its most recent improvement based on the Wirtinger integral inequality. The potential capability of this approach is demonstrated through applications to stability analysis of time‐delay systems. More precisely, by using the newly derived inequalities, they establish new stability criteria for two classes of time‐delay systems, namely discrete and distributed constant delays systems and interval time‐varying delay systems. The resulting stability conditions are derived in terms of linear matrix inequalities, which can be efficiently solved by various convex optimisation algorithms. Numerical examples are given to show the effectiveness and least conservativeness of the results obtained in this study.
Author	Hien, Le Van Trinh, Hieu
Author_xml	– sequence: 1 givenname: Le Van surname: Hien fullname: Hien, Le Van email: hienlv@hnue.edu.vn organization: 1Department of Mathematics, Hanoi National University of Education, Hanoi, Vietnam – sequence: 2 givenname: Hieu surname: Trinh fullname: Trinh, Hieu organization: 2School of Engineering, Deakin University, Geelong, VIC 3217, Australia
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Snippet	In this study, the authors derive some new refined Jensen-based inequalities, which encompass both the Jensen inequality and its most recent improvement based... In this study, the authors derive some new refined Jensen‐based inequalities, which encompass both the Jensen inequality and its most recent improvement based...
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SubjectTerms	Algorithms Brief Papers Constants convex optimisation algorithms convex programming Criteria Delay delays discrete distributed constant delays systems Inequalities interval time‐varying delay systems linear matrix inequalities Optimization refined Jensen‐based inequality approach Stability Stability analysis stability criteria time‐varying systems Wirtinger integral inequality
Title	Refined Jensen-based inequality approach to stability analysis of time-delay systems
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