本論文我們放寬T-S模糊離散系統穩定化設計之條件。我們利用切換式T-S離散模糊系統並且狀態空間會分割成數個局部空間。利用最大狀態間距的概念及片段連續型李亞普諾夫二次式(piecewise quadratic Lyapunov function)在穩定化設計的過程中將可放寬切換式T-S模糊系統的穩定條件。為了避免計算最大狀態間距及設計控制器時疊代運算的問題，我們使用控制輸入限制的方法計算出最大狀態間距。透過MATLAB LMI toolbox，將可以同時設計出合適的控制器增益值以及找到正定矩陣 。最後，透過數值及實際自走車的模擬證明論文理論為有效的方法。

We relax stabilization conditions for a T-S fuzzy discrete system in this thesis. We use switching T-S fuzzy system and the state space of the T-S fuzzy system is divided into several subregions. We can use the concept of the maximal distance of the two continuous state space and the piecewise quadratic Lyapunov function to relax stabilization conditions for a switching T-S fuzzy system. In order to avoid the problem of the maximal distance of the two continuous state space and control gains iteration computing, we use the method of the constraint of a control input to count maximal distance of the two continuous state space. We design suitable the controller and find out the positive definite matrices   at the same time by using MATLAB LMI toolbox. Finally, we utilize the simulations of numerical example and practical example to prove the effectiveness of this method.

目錄
中文摘要	I
英文摘要	II
目錄	III
圖目錄	V
第一章	緒論	1
1.1 研究背景與目的	1
1.2 論文具體成果	4
1.3 論文章節架構	4
第二章	T-S模糊系統穩定性分析及穩定化設計	6
2.1 T-S模糊系統穩定條件	6
2.2 模糊控制器設計	9
2.3 片段連續型李亞普諾夫二次式	13
2.4 切換式T-S模糊系統	17
2.5 結論	19
第三章	放寬系統穩定化設計之條件	20
3.1 最大狀態間距	21
3.2 控制輸入限制條件	25
3.3 控制輸入限制估算最大狀態間距	28
3.4 結論	30
第四章	模擬	32
4.1 數值模擬	32
4.2 自走車動態系統之轉換	34
4.3 自走車模擬	36
4.4 結論	41
第五章	總結	42
參考文獻	43
圖目錄
圖2.1 模糊規則前件部	7
圖2.2 平行分佈補償示意圖	9
圖2.3  所對應之模糊集合	14
圖2.4 模糊集合及分割的子空間	15
圖3.1 歸屬函數	22
圖3.2 觸發區域與 =1之關係圖	22
圖4.1 數值模擬之歸屬函數	32
圖4.2 狀態空間	33
圖4.3 二維收斂軌跡圖	34
圖4.4 自走車運動系統	35
圖4.5 自走車系統之模糊建模	36
圖4.6原模型狀態變數平面圖	38
圖4.7 近似模型狀態變數平面圖	38
圖4.8 近似模型與原模型之誤差平面圖	39
圖4.9 自走車收斂軌跡圖一	40
圖4.10 自走車收斂軌跡圖二	41

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