本論文旨在提升H2及H∞強健控制理論的可理解性與教學應用價值，針對現有文獻中常見的推導不易理解、邏輯關係不清與輔助工具導引不足等問題，進行整理與改進。本文提出三項主要目標：(一)釐清H2及H∞控制器設計的邏輯架構與設計條件；(二)建立線性分式轉換(Linear Fractional Transformation, LFT)與鍊散射描述(Chain Scattering Description, CSD)兩種設計方法間的步驟與數學對應關係；(三)開發具教學導向與視覺化輔助功能的圖形使用者介面(Graphical User Interface, GUI)，協助使用者掌握設計流程與系統行為。在理論方面，本文重新解釋H2及H∞控制的設計邏輯，並比較LFT與CSD方法在架構與數學表達上的差異，彌補文獻中對兩法整合不足的缺口。同時分析CSD法中兩種典型結構的閉迴路行為，並以理論驗證其穩定性一致性。工具方面，本研究以MATLAB為基礎開發GUI，強化學習與實作的連結。本論文有助於降低H2及H∞強健控制的學習門檻，提升設計流程的透明度與可操作性，並提供一套具教學與實務應用的輔助平台，促進理論與應用的有效結合。

This thesis aims to improve the clarity and educational accessibility of H2 and H∞ robust control theory by addressing common challenges such as complex derivations, unclear design logic, and insufficient practical design guidance. The research pursues three main objectives: (1) clarifying the design rational and conditions of H2 and H∞ controllers; (2) establishing step-by-step and mathematical correspondences between Linear Fractional Transformation (LFT) and Chain Scattering Description (CSD) methods; and (3) developing an educational and visual MATLAB-based Graphical User Interface (GUI). On the theoretical side, the study reformulates robust control design procedures, compares LFT and CSD structures, and highlights their integration potential. It also analyzes the closed-loop relation of two CSD configurations, proving their theoretical equivalence and clarifying their roles in controller and observer design. On the practical side, the proposed GUI allows users to interactively explore system responses, fine-tune design parameters, and visualize the effects of spectral zeros and pole placement. By bridging theory and practice, this research lowers the learning barrier, enhances design transparency, and provides a useful platform for teaching and practical application of H2 and H∞ robust control.

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