  ### 博碩士論文 103323073 詳細資訊

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(H∞ Static Output Feedback Controller Design of Fuzzy Systems Via Homogeneous Euler′s Method)

 ★ 強健性扇形區域穩定範圍之比較 ★ 模糊系統混模強健控制 ★ T-S模糊模型之建構、強健穩定分析與H2/H∞控制 ★ 廣義H2模糊控制-連續系統 線性分式轉換法 ★ 廣義模糊控制-離散系統 線性分式轉換法 ★ H∞模糊控制－連續系統 線性分式轉換法 ★ H∞模糊控制—離散系統 線性分式轉換法 ★ 強健模糊動態輸出回饋控制-Circle 與 Popov 定理 ★ 強健模糊觀測狀態回饋控制-Circle與Popov定理 ★ H_infinity 取樣模糊系統的觀測型控制 ★ H∞取樣模糊系統控制與觀測定理 ★ H-ihfinity取樣模糊系統動態輸出回饋控制 ★ H∞模糊系統控制-多凸面法 ★ H∞模糊系統控制-寬鬆變數法 ★ 時間延遲 T-S 模糊系統之強健 H2/H(Infinity) 控制與估測 ★ 寬鬆耗散性模糊控制-波雅定理

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V (x) = x′P(x)x = 1/(g(g-1))x′∇xxV (x)x。

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.

★ 平方和
★ Takagi-Sugeno模糊系統
★ 尤拉齊次多項式定理
★ H∞狀態回授控制
★ H∞靜態輸出回授控制

★ sum of squares
★ T-S fuzzy systems
★ Euler′s Theorem for Homogeneous Function
★ H∞ state feedback control
★ H∞ static output feedback control

1、背景介紹......................................................................... 1
1.1 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 論文結構. . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 符號標記. . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 預備定理. . . . . . . . . . . . . . . . . . . . . . . . 5
2、系統架構與檢測條件...................................................... 7
2.1 模糊系統架構簡介. . . . . . . . . . . . . . . . . . . 7
2.2 尤拉齊次多項式定理. . . . . . . . . . . . . . . . . 8
2.3 H1 狀態/靜態輸出迴授控制系統. . . . . . . . . . . 12
2.4 主要定理. . . . . . . . . . . . . . . . . . . . . . . . 17
3、模糊建模方法及平方和檢測法........................................ 24
3.1 泰勒級數模糊. . . . . . . . . . . . . . . . . . . . . 24
3.2 平方和檢驗法. . . . . . . . . . . . . . . . . . . . . 26
3.3 平方和檢驗法之定理2.1 穩定度條件. . . . . . . . . 30
3.4 平方和檢驗法之定理2.2 穩定度條件. . . . . . . . . 31
4、電腦模擬......................................................................... 34
4.1 例題一. . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 例題二. . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 例題三. . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 例題四. . . . . . . . . . . . . . . . . . . . . . . . . 53
5、結論與未來方向.............................................................. 59
5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 未來研究方向. . . . . . . . . . . . . . . . . . . . . 61

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