Improved stability criteria for linear systems with interval time-varying delays: Generalized zero equalities approach

This paper suggests first-order and second-order generalized zero equalities and constructs a new flexible Lyapunov–Krasovskii functional with more state terms. Also, by applying various zero equalities, improved stability criteria of linear systems with interval time-varying delays are developed. U...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 292; pp. 336 - 348
Main Authors Lee, Seok Young, Lee, Won Il, Park, PooGyeon
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2017
Subjects
Interval time-varying delays
LMI
Stability analysis
Wirtinger-based integral inequality
Zero equality
Wirtinger-based integral inequality
Zero equality
LMI
Stability analysis
Interval time-varying delays
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Summary:This paper suggests first-order and second-order generalized zero equalities and constructs a new flexible Lyapunov–Krasovskii functional with more state terms. Also, by applying various zero equalities, improved stability criteria of linear systems with interval time-varying delays are developed. Using Wirtinger-based integral inequality, Jensen inequality and a lower bound lemma, the time derivative of the Lyapunov–Krasovskii functional is bounded by the combinations of various state terms including not only integral terms but also their interval-normalized versions, which contributes to make the stability criteria less conservative. Numerical examples show the improved performance of the criteria in terms of maximum delay bounds.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2016.07.015