H∞模糊系統控制-多凸面法

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姓名

李豐州(Fong-Jhou Li) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

H∞模糊系統控制-多凸面法
(H∞ Stabilization Analysis - Multiconvexity Approach)

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摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 共同P解
★ 線性矩陣不等式
★ 多凸面
★ 李亞普諾夫方程式
★ 狀態回饋控制
★ 非共同P解
★ T-S模糊模型

關鍵字(英)

★ multiconvexity
★ Takagi-Sugeno(T-S)
★ Lyapunov function
★ LMI
★ Common P
★ Non-common P
★ state feedback control

論文目次

第一章簡介 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 3
1.5預備定理 4
1.6線積分法 5
第一部份:李亞普諾夫穩定(Lyapunov Theorem) 8
第二章系統架構與穩定條件 8
2.1系統架構 8
2.2穩定條件 9
第三章狀態回饋控制器設計 25
3.1系統架構 25
3.2狀態回饋控制器 26
3.2.1連續系統 26
3.2.2離散系統 31
第四章電腦模擬 34
4.1連續系統 34
4.1.1系統架構 34
4.1.2求解 35
4.2離散系統 39
4.2.1系挺架構 39
4.2.2求解 39
第二部分: H∞定理 43
第五章系統架構與H∞定理 43
5.1系統架構 43
5.2狀態回饋控制器 44
5.3檢測條件 45
5.3.1連續系統 45
5.3.2離散系統 57
第六章電腦模擬 63
6.1連續系統 63
6.1.1系統架構 63
6.1.2求解 64
6.2離散系統 68
6.2.2系統架構 68
6.2.2求解 69
第七章結論與未來方向 71
7.1總結 71
7.2未來研究方向 71
參考文獻 72

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指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2006-6-30

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