在自動控制系統中，常使用觀測器重建無法直接量測之系統內部狀態或估測外部擾動。然而，傳統觀測器的性能高度仰賴受控體模型之準確性，容易受到模型不確定性與量測雜訊的影響。因此，本研究採用H2控制與H∞控制理論進行觀測器設計，以提升觀測器之強健性與抗擾能力。為強化設計結果之可預測性，本文採用轉移函數形式進行分析，並結合頻譜分解與互質因式分解等方法，探討設計權重與閉迴路極點、頻寬及頻域響應間之關聯，使設計者能於控制器求解前預測系統特性。本文針對輸出注入模型與輸出估測模型兩種特殊案例進行分類，並分析兩者於觀測器設計問題中所適用之情境。為確保所提出設計架構於實務應用上的可行性，本文導入即時模擬，進一步評估觀測器於離散化後之性能表現。本文所建立之分析流程，將有助於提升強健觀測器設計過程之可預測性，並提供設計者進行權重選擇與性能調校之依據。

Observers are widely used in feedback control systems to reconstruct unmeasurable internal states and estimate external disturbances. However, the performance of conventional observers depends the accuracyof the plant model and is often degraded by measurement noise. To address these limitations, this study emplys H2 and H∞ control theories to develop several observer design frameworks. Through spectral factorization and coprime factorization, the relationships among weighting functions, closed-loop poles, observer bandwidth, and frequency-domain characteristics are systematically investigated. This analytical approach allows designers to predict system characteristics before synthesizing the controller. Furthermore, two special problems, namely the output injection (OI) and the output estimation (OE) problems, are considered, and their applicability to different observer design problems is discussed. The effectiveness of the proposed frameworks is demonstrated using real-time simulations. Overall, the proposed analytical procedures provide a unified framework for observer design and facilitate the prediction of observer performance through appropriate selection of weighting functions.

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