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Student Number 953203060 Author Jia-ren Wan(萬嘉仁) Author's Email Address No Public. Statistics This thesis had been viewed 1291 times. Download 345 times. Department Mechanical Engineering Year 2007 Semester 2 Degree Master Type of Document Master's Thesis Language zh-TW.Big5 Chinese Title Relaxed, dissipative fuzzy control - Polya theorem Date of Defense 2008-06-20 Page Count 100 Keyword Dissipative control Linear matrix inequality Polya's theorem Relaxed condition T-S model Abstract In this thesis, we propose a general quadratic dissipative state feedback control method to solve a stabilization problem for fuzzy system with sector-bounded type nonlinearities at the input.

The problem covers the bounded real, positive real and sector-bounded performance as a special case by choosing the corresponding quadratic supply rate.

Moreover, we also prove necessary and sufficient conditions to state feedback controllers ensuring quadratic stability for Takagi-Sugeno fuzzy systems in theory.

But our main objective is to generate a family of linear matrix inequalities based on an extension of Polya theorem (a.k.a. Matrix-valued Polya theorem).

The proposed conditions are stated as progressively less conservative sets of linear matrix inequalities,

allowing us to obtain a solution for the quadratic stabilizability problem whenever a solution exists.

At last, an additional relaxed condition is also provided, relying on the use of slack matrix variables.

All proposed methods will be shown via theoretical analysis and numerical simulations.Table of Content 論文摘要 i

Abstract iv

誌謝 v

圖目 x

第一章 簡介 1

1.1 文獻回顧 1

1.2 研究動機 3

1.3 論文結構 4

1.4 符號標記 5

1.5 預備定理 7

1.6 耗散性之物理意義 8

第一部份:耗散性控制(Dissipativecontrol) 13

第二章 系統架構與耗散性檢測條件 13

2.1 系統架構 13

2.1.1 廣義非線性系統 13

2.1.2 非線性模糊系統 15

2.2 檢測耗散性條件 16

第三章 有界非線性輸入控制器之設計 23

3.1 有界非線性輸入系統 23

3.2 狀態回饋控制器 25

第四章 電腦模擬一 32

4.1 連續系統 32

4.1.1 系統模型 32

4.1.2 求解 34

4.2 離散系統 40

4.2.1 系統模型 40

4.2.2 求解 43

第二部份:波雅定理之代數應用 50

第五章 模糊閉迴路系統之充要條件 50

5.1 波雅定理(P′olya’sTheorem) 50

5.2 矩陣波雅定理(Matrix-valued P′olya's Theorem) 52

5.3 範例及寬鬆性 56

第六章 電腦模擬二 58

6.1 解空間 58

6.2 倒單擺系統 63

6.2.1 系統描述 63

6.2.2 求解 63

第三部份:具鬆弛矩陣變數之寬鬆環境 68

第七章 波雅定理之寬鬆環境 69

7.1 鬆弛矩陣變數 69

7.2 範例 76

第八章 電腦模擬三 82

8.1 解空間比較 82

8.1.1 連續系統 82

8.1.2 離散系統 86

8.2 耗時比較 90

第九章 結論與未來研究方向 91

9.1 總結 91

9.2 未來研究方向 92

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