Open AccessRefined Jensen‐based inequality approach to stability analysis of time‐delay systems
Author(s) -
Van Hien Le,
Trinh Hieu
Publication year - 2015
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2014.0962
Subject(s) - jensen's inequality , mathematics , linear matrix inequality , stability (learning theory) , inequality , control theory (sociology) , interval (graph theory) , regular polygon , constant (computer programming) , convex combination , stability criterion , convex optimization , discrete time and continuous time , mathematical optimization , computer science , convex analysis , control (management) , mathematical analysis , statistics , geometry , machine learning , artificial intelligence , combinatorics , programming language
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.