A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems

This paper focuses on the delay-dependent stability problem of time-varying delay systems. A generalized free-matrix-based integral inequality (GFMBII) is presented. This inequality is able to deal with time-varying delay systems without using the reciprocal convexity lemma. It overcomes the drawbac...

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Bibliographic Details
Published in:	Applied mathematics and computation Vol. 354; pp. 1 - 8
Main Authors:	Zeng, Hong-Bing, Liu, Xiao-Gui, Wang, Wei
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.08.2019
Subjects:	Free-matrix-based integral inequality(FMBII) Linear matrix inequality Stability Time-varying delay Linear matrix inequality Free-matrix-based integral inequality(FMBII) Stability Time-varying delay
ISSN:	0096-3003, 1873-5649
Online Access:	Get full text
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Summary:	This paper focuses on the delay-dependent stability problem of time-varying delay systems. A generalized free-matrix-based integral inequality (GFMBII) is presented. This inequality is able to deal with time-varying delay systems without using the reciprocal convexity lemma. It overcomes the drawback that the Bessel–Legendre inequality is inconvenient to cope with a time-varying delay system as the resultant bound contains a reciprocal convexity. Through the use of the derived inequality and by constructing a suitable Lyapunov–Krasovskii function (LKF), improved stability criteria are presented in the form of linear matrix inequalities (LMIs). Two numerical examples are carried out to demonstrate that the results outperform the state of the art in the literature.
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2019.02.009