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This paper deals with the problem of stability for aperiodically sampled-data control systems with constant communication delays. Less conservative results are derived by two main techniques. First, a new looped-functional-based Lyapunov function is proposed, which considers the information of intervals <inline-formula> <tex-math notation="LaTeX">$x({t_{k}})$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$x(t)$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$x(t)$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$x({t_{k + 1}})$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$x(t_{k}-\tau)$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$x(t-\tau)$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$x(t-\tau)$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$x(t_{k+1}-\tau)$ </tex-math></inline-formula>. Second, in the derivative of the Lyapunov function, the integral term which has the information of sampling-period plus communication delay is divided into three parts. Then, by employing integral inequality techniques, some improved stability conditions are derived. The numerical examples demonstrate the validity of the proposed methods.