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

摘要

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. (C) 2020 Elsevier Inc. All rights reserved.