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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Published in:IET control theory & applications Vol. 9; no. 14; pp. 2188 - 2194
Main Authors: Hien, Le Van, Trinh, Hieu
Format: Journal Article
Language:English
Published: The Institution of Engineering and Technology 17.09.2015
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1751-8644
1751-8652
DOI:10.1049/iet-cta.2014.0962