擾動的來源主要是由於下述幾種原因：系統的非線性關係，為了簡單起見而簡化原來較複雜的系統所帶來的誤差問題、系統參數的變動、周遭客觀環境的改變、不可避免的資料誤差等等都是可能的擾動原因。
除了擾動問題外，另一種可能使系統的穩定性降低的就是時間延遲的存在。時間延遲不僅發生在物理、工程或化學等方面的系統，同時也可能出現在政治或經濟方面等之系統。因為由於時間延遲的出現改變了系統的特性方程式，因此要解決上述系統由於時間延遲的介入也就變得非常複雜了。
因此，如通訊系統、化工程序、電力系統、運輸系統等，皆是擾動時延系統的例子。本文主要針對一個線性相依的擾動時延系統做穩定性的評估與探討，主要分成兩方面內容如下：
（1） 非結構化擾動時延系統
（2） 結構化擾動時延系統
本文在擾動時延系統穩定度分析中，主要採用Lyapunov Stability Theorem, Matrix Measure Function 及 Kharitonov Theorem等方法來改進先前對非結構化及結構化擾動時延系統的穩定性分析及探討，並對時延擾動系統作迴授控制器設計，使我們對此系統能更確認系統的穩定度。
本論文的研究主要就是對上述的狀況作一較完整的分析與設計。我們期望能夠得到一個較佳的穩定準則及較精確的條件，並設計控制器增加系統的穩定度。

In this thesis, we deal with the time-delay system with uncertainty. We comment on the previous papers [5], [9] and modify the results. Besides, we present better criteria which are proven to be less conservative than previous results in the literatures. Besides, we present other stability criteria which can deal with different systems. The feedback controller can be designed by optimal method. Kharitonov theorem and edge theorem can help us to reduce the calculation. As a result, we obtained the allowable delay time for the system with unstructured and highly structured uncertainty and designed a feedback controller to further ensure its stability

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