本篇論文可分為兩大部分來進行討論，以不同形式的控制條件來研究相同系統的控制問題，其中第一部份是以三階 (cubic) 的形式來進行系統的分析與研究，而第二部份則是以二階 (quadratic) 的形式來對系統進行分析討論，其中兩者都是以蕭氏轉換 (Schur complement) 及全等轉換 (congruence transformation) 的方式對控制問題進行轉換之後的分析與推導。
論文中所研究的是一個含有分式項的模糊系統控制問題，以線性分式轉換 (Linear fractional transformation, LFT) 為架構的動態輸出回饋控制器來使其穩定，並滿足廣義H2 (Generalized H2) 性能指標的要求。其分析最主要的方式是應用全等轉換的技巧來進行控制器的分析與設計，使含有分式項的模糊系統能達到穩定並滿足廣義 H2 的性能指標問題。在這個部分中，我們將控制器的架構以三階與二階兩種不同形式的方式表現出來。經過全等轉換之後，我們分別可以得到兩組線性矩陣不等式 (Linear matrix inequalities, LMIs) 來對原本的控制問題求解。除了上述兩個線性矩陣不等式外，我們還要考慮比例條件 (scaling condition) 的限制。然後，以一個球桿系統的例子來進行電腦模擬。最後舉一個含有不確定項的模糊系統來印證 LFT模糊系統是可以用來討論含有不確定項的模糊系統，以質簧系統的例子來進行電腦模擬分析。

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