本論文主要研究連續模糊系統之靜態輸出回授控制器設計，使用
非二次李亞普諾夫函數(non-quadratic Lyapunov function) 及其對時間的變化率做為穩定的條件, 並滿足H1 性能指標。本論文分為兩個步驟設計靜態輸出回授控制器，步驟一: 求得狀態回授增益，使用二
次李亞普諾夫函數(quadratic Lyapunov function) ，步驟二: 求解靜態輸出回授增益, 使用非二次李亞普諾夫函數(non-quadratic Lyapunov function)，其中以尤拉齊次多項式定理建立非二次李亞普諾夫函數(non-quadratic Lyapunov function)，其形式為
V (x) = x'P(x)x = 1/(g(g-1))x'∇xxV (x)x。
電腦模擬方面以平方和方法(Sum-of-Squares) 來檢驗模糊系統的
穩定條件，並設計出狀態回授控制器以及靜態輸出回授控制器。

The main contribution in this thesis is static output feedback controller
design of H1 continuous fuzzy system. And we can solve the inequalities derived from non-quadratic Lyapunov function and its time gradient. It’s a two-step procedure for solving output feedback control gain, step 1: solve for state feedback gain (for common P theorem), step 2: solve for static output feedback gain (for homogeneous polynomial P(x) theorem). A non-quadratic Lyapunov function derived from
Euler’s homogeneous polynomial theorem has following form
V (x) = x'P(x)x = 1/(g(g-1))x'∇xxV (x)x。
In numerical simulation, we solve for state feedback gain first and then solve for static output feedback gain with sum-of-squares approach.

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