本論文，基於李亞普諾夫函數，進一步推導出新的穩定性準則於具有時變延遲時延系統。藉由李亞普諾夫函數來建構穩定準則，將延遲函數的微分上界加入Lyapunov-Krasovskii泛函來降低準則的保守性。針對具有快速變動的時變時間延遲系統也可直接處理，確保強健性穩定在最大允許上界的區間內。目前文獻方法對離散時延h(t)的處理要求其導數必須小於1,即：h&(t)<1，這在一定程度上使所得結果的應用有一定的局限性。本論文的主要貢獻如下：1.利用積分不等式和時延分解法結合Lyapunov-Krasovskii泛函於具有時變延遲時延系統之穩定度問題。利用牛頓–布尼茲公式中各項的關係，首次對此系統之強健穩定度提出時延相關的強健穩定性準則。2.利用時延分解結合Lyapunov-Krasovskii泛函方法，探討了此系統的穩定性。通過對時延進行分解，使得每一部分均依不同的Lyapunov泛函，分別獲得了系統時延相關的穩定性充分條件。

This paper studies the problem of stability for systems with differentiable time-varying delays. By using the information of delay derivative, improved asymptotic stability conditions for time-delay systems are presented. Unlike the previous methods, the upper bound of the delay derivative is taken into consideration even if this upper bound is larger than or equal to 1( h t() 1 & < ). It is proved that the obtained results are less conservative than the existing ones. Meanwhile, the computational complexity of the presented stability criteria is reduced greatly since fewer decision variables are involved. Numerical examples are given to illustrate the effectiveness and less conservatism of the obtained stability conditions.