本論文是以狀態回饋控制研究模糊系統(fuzzy systems) 的穩定性問題，本論文將分為兩部分來進行討論，第一部份先推導滿足 Lyapunov 穩定的檢測條件，第二部分考慮干擾的影響，推導出滿足 H∞ 穩定的檢測條件 。
本論文將在 LMI(Linear Matrix Inequality) 中探討一個新的降低保守性穩定度檢測條件，連續及離散模糊系統將由統一的方法來論述。藉由建立在李亞普諾夫函數 (Lyapunov function)及結合多凸面 (multi-convexity) 的概念，我們可降低一般普遍存在於共同P矩陣 (common P) 論述上的保守性，然而本論文是建立在非共同P解 (non-common P) 的論述上，因此具有更寬鬆的求解條件。
本論文在控制的部分是研究一非線性系統受到狀態回饋控制器控制 ， 首先將此非線性系統轉換成 Takagi-Sugeno(T-S) 模糊系統 ，
以提供一套系統化的研究方法 , 研究非線性系統的穩定性分析問題 。 針對 T-S 模糊模型 ,
本論文根據非平行分散式補償器 (Non PDC) 的概念設計狀態回饋控制器 ,
再以 Lyapunov 定理及多凸面的概念 , 求得滿足系統穩定的條件 。

A new stabilization condition guaranteeing H∞
performance of T-S fuzzy control systems is studied in this paper, continuous- and discrete-time fuzzy control systems treated in a unified manner.
A premise-dependent Lyapunov function is chosen and the quadratic property of the premise
(i.e. grade of membership, μ) is considered in the stabilization analysis.
The stabilization analysis is performed on the basis of Lyapunov theory and multiconvexity,
here stated using LMI to profit from the advantage of convex optimization.
It is shown, via theoretical analysis and numerical simulations, that our results are much
less conservative than existing reports in the literature.

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