Abstract
This paper focuses on the problem of delay-dependent stability of linear systems with time-varying delays. Firstly, a new free-matrix-based inequality is proposed, which is an improved version of Bessel-Legendre inequality. This inequality is applicable to time-varying-delay systems. It overcome the drawback the resulting bounds inevitably include the reciprocal convexity when employing the Bessel-Legendre inequality to deal with time-varying-delay systems. Based on the novel inequality proposed and by constructing an appropriate Lyapunov- Krasovskii functional (LKF), improved stability criteria are presented in a sets of linear matrix inequalities (LMIs). Numerical examples suggest that the results outperform the state of the art in the literature.
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