| Summary: | Abstract The stability problem of linear systems with time-varying delays is studied by improving a Lyapunov–Krasovskii functional (LKF). Based on the newly developed LKF, a less conservative stability criterion than some previous ones is derived. Firstly, to avoid introducing the terms with h2(t) $h^{2}(t)$, which are not convenient to directly use the convexity of linear matrix inequality (LMI), the type of integral terms {∫stx˙(u)du,∫t−hsx˙(u)du} $\{\int _{s}^{t}\dot{x}(u)\,du, \int _{t-h}^{s}\dot{x}(u)\,du\}$ is used in the LKF instead of {∫stx(u)du,∫t−hsx(u)du} $\{\int _{s}^{t}x(u)\,du, \int _{t-h}^{s}x(u)\,du\}$. Secondly, two couples of integral terms {∫stx˙(u)du,∫t−h(t)sx˙(u)du} $\{\int _{s}^{t}\dot{x}(u)\,du, \int _{t-h(t)}^{s}\dot{x}(u)\,du\}$, and {∫st−h(t)x˙(u)du,∫t−hsx˙(u)du} $\{\int _{s}^{t-h(t)}\dot{x}(u)\,du, \int _{t-h}^{s}\dot{x}(u)\,du\}$ are supplemented in the integral functionals ∫t−h(t)tx˙(u)du $\int _{t-h(t)}^{t}\dot{x}(u)\,du$ and ∫t−ht−h(t)x˙(u)du $\int _{t-h}^{t-h(t)}\dot{x}(u)\,du$, respectively, so that the time delay, its derivative, and information between them can be fully utilized. Thirdly, the LKF is further augmented by two delay-dependent non-integral items. Finally, three numerical examples are presented under two different delay sets, to show the effectiveness of the proposed approach.
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