本論文是以狀態回饋控制(state feedback control)研究受控體(fuzzy systems) 所代表的模糊系統穩定與否問題，以及應用波雅定理((P´olya theorem) 於穩定性檢測條件上，以得到較為寬鬆的檢測條件。
內容方面本論文將分為兩部分來進行討論，第一部份為利用多凸面法(multi-convexity)，推導滿足Lyapunov穩定性的檢測條件，並加入波雅定理(P´olya theorem)，藉由此方法得到更大的解空間，並利用LMI (Linear Matrix Inequality)求解，第二部份為利用平方和SOS (Sum Of Squares)求解。
第一部分為利用多凸面(multi-convexity)的概念，降低一般普遍存於共同P矩陣(common P)論述上的保守性，本論文是建立在非共同$P$解(non-common P)的論述上，並且應用波雅定理(P´olya theorem)加上寬鬆變數(Relaxed variables)，因此具有更寬鬆的求解條件。
第二部份，近年來應用於求解的工具，大多以LMI(Linear Matrix Inequality)求解，但其複雜度會隨著矩陣大小以及LMI個數而增大，而利用SOSTOOLS求解則能大大降低其複雜度並且不用額外的寬鬆變數(Relaxed variables)。

Based on parameter-dependent Lyapunov function, we study asymptotically copositive relaxation families with certificate of convergence to the existence of parameter-dependent Lyapunov function, releasing the conservatism that commonly exists in the quadratic stability approaches.

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