本篇論文主要研究連續時間模糊(fuzzy)系統的非二次穩定寬鬆條件，我們利用波雅定理的代數性質加上寬鬆矩陣變數(slack matrix variables)，再利用激發強度的多項式排列控制器與估測器，並做控制與估測之相關分析，利用這些條件來建立一組寬鬆的線性矩陣不等式(LMI)並且降低求解的保守性。

論文還將透過非二次(non-quadratic)穩定的分析加上寬鬆矩陣變數(slack matrix variables)的使用，使得此組線性矩陣不等式(LMI)的求解保守性更進一步的降低，然後再將其中加入的寬鬆矩陣變數與波雅的線性矩陣不等式以多項式矩陣型態來表示，在判斷式子中加入了寬鬆矩陣變數，運用多項式矩陣型態之特性，將同階數的元素放在矩陣對角線上或同階數之非對角線上作變化，使判斷式保守度降低。

In this thesis, we investigate non-quadratic relaxation for continuous-time fuzzy observed-state feedback control systems, which are characterized by parameter-dependent LMIs (PD-LMIs), exploiting the algebraic property of Polya Theorem to construct a family of finite-dimensional LMI relaxation with righ-hand-side slack matrices that release conservatism. And we use matrix-values HPPD function of degree g on Lyapunov function that release conservatism. Lastly, Numerical experiments illustrate this method can provide the advantage of relaxations, being less conservative and effective.

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