本篇論文以線性分式轉換法為主軸，分成三大部分來討論，第一部分是以數學模型來做推導，經由H∞性能條件和比例條件，推導出兩個矩陣不等式，第二部分為三次參數化和二次參數化，第三部分則是例子的電腦模擬，將依序來做介紹。
第一部分，會先介紹線性分式轉換系統的架構和特徵以及因為線性分式轉換法架構而產生的比例條件。針對H∞性能條件和比例條件經由一些推導可得到兩個矩陣不等式，我們利用這兩個式子求出滿足條件式的控制器增益和一些變數，且可得知系統達到穩定，並滿足H∞性能指標要求。
第二部分為三次參數化和二次參數化，兩者皆為將第一部分所推導出來的線性矩陣不等式，歸納成一個定理，不過其所用的寬鬆方法不同，也推導出不同架構的線性矩陣不等式，因而分別歸納成一個定理。
最後以一個倒車入庫的例子進行電腦模擬分析，我們先將其非線性系統推導成一個擁有線性分式轉換法架構的式子，再利用所得到的參數去求解，用圖來顯示模擬的結果，以對定理做個驗證。

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