本論文是研究延遲模糊系統(fuzzy systems) 所代表的系統穩定問題，
以及應用波雅定理於檢測條件上，來得到一較為寬鬆的檢測條件。
內容方面本論文將分為兩部分來進行討論， 第一部份先推導一般性的延遲穩定條件， 第二部分引入狀態擴充的延遲穩定條件， 再引入多輸入延遲加以驗證波雅定理的應用。
本論文將在 LMI(Linear Matrix Inequality) 中探討一個時間延遲系統的穩定檢測條件。
藉由建立在Lyapunov-Krasovskii函數， 將目前文獻中尚未完全處理的延遲參數， 做一個完全性的整合。
並解決了傳統上延遲參數為時變的狀況， 將微分後難以求解的積分項問題， 重新整理以求得穩定解。
本論文同時也研究當輸入延遲增加的情況下， 考慮系統的穩定情形， 加入寬鬆環境下的條件並加以驗證波雅定理的實際應用。
本論文提供一套系統化的研究方法，研究延遲系統的穩定條件，並將在最後代入波雅定理探討求解的檢測條件，
進而達到Lyapunov-Krasovskii穩定的充要條件。

In this study, a stabilization problem for continuous-time fuzzy systems
subject to multiple time-varying delays in both state and input variables is addressed.
The main objective is to design a stablilizing controller that stabilizes the aforementioned delay system.
Based on Lyapunov-Krasovskii functional and P''olya theorem, sufficient stabilization conditions are stated in terms of
LMIs. Therefore, stabilizing controllers can be obtained easily with existing convex algorithms. Unlike existing methods,
polynomial theory is used to deal with input-delay term since this delay term introduces
an additional summation after defuzzification.
Lastly, three examples are given to illustrate
the advantages of the proposed machinery, yielding more relaxations when compared to existing methods.

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