New versions of Bessel–Legendre inequality and their applications to systems with time-varying delay

Jun Chen and Ju H. Park

Applied Mathematics and Computation, 2020, vol. 375, issue C

Abstract: This paper is concerned with the stability of linear time-delay systems by applying the Lyapunov–Krasovskii (L–K) functional method. Two versions of Bessel–Legendre (B-L) inequality are developed that are more suitable to deal with the stability problem of systems with a time-varying delay. Meanwhile, in order to take full advantage of the interest of the new versions of B-L inequality, a novel L–K functional is properly tailored by integrating the integral information of the state into quadratic and integral terms. As a result, more relaxed stability conditions are obtained, whose effectiveness is illustrated by two commonly-used numerical examples.

Keywords: Bessel–Legendre inequality; Lyapunov–Krasovskii functional; Stability; Time-delay system (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:375:y:2020:i:c:s0096300320300291

DOI: 10.1016/j.amc.2020.125060

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