Reducing conservatism of stability criteria for linear systems with time-varying delay using an improved triple-integral inequality

作者：

Highlights：

• An improved triple-integral inequality is introduced, which can provide a tighter bound than some existing ones when estimating some triple-integral terms.

• Two novel Lyapunov-Krasovskii functionals are introduced, catering for two cases of time-varying delay, where the time-varying delay is either differentiable or uniformly continuous.

• By employing the recent necessary and sufficient condition on quadratic matrix polynomial inequalities, two cases of time-varying delays are discussed. As a result, two stability criteria for two cases of time-varying delay are obtained, which are demonstrated to be of less conservatism than some existing results.

摘要

•An improved triple-integral inequality is introduced, which can provide a tighter bound than some existing ones when estimating some triple-integral terms.•Two novel Lyapunov-Krasovskii functionals are introduced, catering for two cases of time-varying delay, where the time-varying delay is either differentiable or uniformly continuous.•By employing the recent necessary and sufficient condition on quadratic matrix polynomial inequalities, two cases of time-varying delays are discussed. As a result, two stability criteria for two cases of time-varying delay are obtained, which are demonstrated to be of less conservatism than some existing results.

论文关键词：Time-varying delay,Integral inequality,Stability,Lyapunov–Krasovskii functional

论文评审过程：Received 15 December 2019, Revised 9 February 2020, Accepted 22 March 2020, Available online 16 April 2020, Version of Record 16 April 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125254