本篇論文在Takagi-Sugeno (T-S) 模糊系統下探討穩定分析與控制器設計，結合模糊區域概念和分段式Lyapunov穩定準則來設計模糊控制器，稱之為分段T-S模糊區域控制器。我們利用模糊區域概念將原來的子系統切割成數個模糊區域，當輸入的瞬間只會有一個模糊區域被觸發。一般利用T-S模糊區域概念所設計之控制器，必須要求出共同的正定矩陣以滿足系統穩定準則。但是，若一非線性系統是由許多的模糊規則數所組成，則共同 可能會難求出。於此，本篇論文利用分段Lyapunov穩定準則只需求出各區域裡的個別正定矩陣，如此降低了判定方法的保守性，分段Lyapunov穩定準則以線性不等式(LMIs)表示，並藉此演算法算出個別區域的Lyapunov 矩陣及區域控制器。
因為分段T-S模糊區域概念有著簡化設計降低保守性及容易實現的優點，所以延伸分段Lyapunov穩定準則與模糊區域概念在不確定系統及觀察器的設計上，目的就是處理模糊區域的強健控制問題及設計對應於每一個模糊區域的觀察增益值，使得整個T-S模糊區域系統得以漸近穩定。再者，我們將利用數個數值例子來說明本論文理論的有效性。

The stability analysis and controller design for T-S fuzzy system are discussed in this thesis. This thesis combines the fuzzy region concept and the piecewise Lyapunov stability criterion to design a new fuzzy controller which is called piecewise T-S fuzzy region controller. We utilized the fuzzy region concept to partition the original plant rules into several fuzzy regions. Only one partial fuzzy region is fired at the instant of each input vector being coming. The original controller design of T-S fuzzy region concept is required to find the common Lyapunov matrix. This common positive definite matrix may not exist when the T-S fuzzy system includes many fuzzy rules. Now we utilize the piecewise Lyapunov stability criterion and the regional concept to find the individual Lyapunov matrix and fuzzy controller for each region. Therefore, this proposed condition is less conservative. The piecewise Lyapunov stability criterion is expressed in terms of Linear Matrix Inequalities (LMIs).
The advantages of the piecewise fuzzy regional concept are less conservative, simpler to design and to be realized easily. In addition, this thesis will extend the piecewise Lyapunov stability criterion and the fuzzy region concept to the controller design of system with uncertainty and observer design. The purposes of this thesis are to address the robust fuzzy region control problem and design the observer rules for each fuzzy region such that the overall fuzzy model are stabilized. Furthermore, numerically examples are given to illustrate the usefulness of the proposed approaches.

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