本論文提出適用於具有未知輸入輸出擾動之未知資料採樣奇異方陣／非方陣系統的一種基於觀測／卡爾曼濾波器鑑別法之線性二次數位追蹤器，和一種新的基於函數型觀測器之離散等效輸入干擾估測器。在本論文中，首先探討即使無脈衝項之奇異線性二次追蹤器的問題有解，但在常見的系統中，可能會使基於追蹤器的廣義代數黎卡笛方程式無解。為了克服這項問題，我們巧妙地採取一種技術，即對奇異系統降階為等效真分正規模型，以解決廣義代數黎卡笛方程式的問題；同時此方法也讓MATLAB無法模擬線性連續奇異系統的時間響應問題，變為可行。之後，對含有未知匹配／不匹配輸入和輸出干擾的資料採樣真分系統，提出基於函數型觀測器的新設計法，以適用一種基於等效真分正規模型的離散等效輸入干擾估測器。最後對整體未知的資料採樣奇異系統，先基於觀測／卡爾曼濾波器鑑別法建立離散等效真分正規模型，接著設計基於預測型狀態估測器的最佳線性二次數位追蹤器，和離散等效輸入干擾估測器；特點在於，不同於大部分類型的未知輸入估測法，採用新的等效輸入干擾估測法已不再侷限於未知干擾的維度。

This thesis presents an observer/Kalman filter identification (OKID) method-based linear quadratic digital tracker (LQDT) and a new functional observer-based discrete equivalent input disturbance (EID) estimator for unknown square/non-square singular sampled-data systems with unknown input and output disturbances. In this thesis, we first indicate that even though the impulsive mode-free singular linear quadratic tracker problem (SLQTP) has a solution, under some quite general cases, the tracker-based generalized algebraic Riccati equation (GARE) might have no solution. To overcome this issue, an ingenious skill, involving the introduced reduced-order equivalent proper regular model (EPRM) of the singular system, is presented to solve for the tracker-based GARE, so that it leads to a potential applicability to a wide class of servo control problems for a singular system. Besides, based on the presented EPRM of the singular system, simulating the time response of continuous linear singular systems to arbitrary inputs, which is not supported by MATLAB, becomes feasible. Furthermore, a new functional observer-based design methodology for the discrete EID estimator of the discrete EPRM has been proposed in this thesis for a proper sampled-data system with unknown matched/mismatched input and output disturbances. Finally, for an unknown singular sampled-data system, the discrete-time version EPRM of the singular sampled-data system is then constructed based on the off-line OKID method, followed by the robust prediction-based state-estimate optimal LQDT associated with the (plug-in) discrete EID for the unknown singular sampled-data system. Foremost, the constraints on the dimension of unknown disturbances existed in a wide class of unknown input estimation methods is eliminated by using the new EID estimation skill.

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