本論文提出針對於資料取樣線性奇異系統的創新型二次式觀測器與軌跡追蹤器的設計法則。首先，利用一些方法把奇異系統轉換成一個對等含有直接傳輸項的系統，再以等效的系統來架構一個高增益的類比二次式軌跡追蹤器,然後利用數位重新設計法則以得到一個低增益且實用的數位軌跡追蹤器，除了數位再設計的方法外，本論文亦提出以直接離散性能指標法來建立軌跡追蹤器的方法，當含有輸入直接傳輸項之連續時間系統的狀態沒辦法有效的被估測時，一個創新型的類比觀測器與對應的數位觀測器在本文中被提出，最後，我們提出數個例子，來說明我們所提出方法的可行性。

This thesis develops novel design methodologies for quadratic observers and trackers of sampled-data linear singular system. At first, some techniques have been utilized to decompose the singular system into an equivalent regular system with a direct transmission term from input to output. Then, a high-gain optimal linear quadratic analogue tracker is proposed based on the equivalent regular system with a direct transmission term from input to output. Subsequently, the prediction-based digital redesign method is utilized to obtain a relatively low-gain and practicably implemental digital tracker. Here, this thesis also derives a method called an alternative digital redesign approach. That this thesis directly discretizes the linear quadratic performance index specified in the continuous-time domain into an equivalent discrete-time performance index for the equivalent regular system with a direct transmission term from input to output. When the state of the continuous-time system with a direct transmission term is not available for measurement, the novel suboptimal analog and its corresponding digital observers are developed for the continuous time and sampled-data linear singular systems, respectively. Several illustrative examples are presented to demonstrate the effectiveness of the proposed design methodology.

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