在本篇論文中針對Takagi-Sugeno (T-S) 模糊模型[1]的系統架構提出了控制器以及估測器的設計方式，並對系統中考慮收斂速度影響時作探討與設計。在控制器部分，我們利用平行分配補償（Parallel Distributed Compensation; PDC）[2]的設計觀念對以T-S 模糊模型描述的非線性受控體作控制器設計，在每一個子系統屬於可控標準式時，我們引用李亞普諾夫(Lyapunov)漸近穩定理論並以李亞普諾夫等式取代李亞普諾夫不等式後，我們可直接獲得李亞普諾夫方程式的解，透過此解便可進一步求到最終的控制器對受控體做控制並達到系統穩定的要求。對於估測器的部分，針對T-S 模糊模型描述的非線性受控體，當每一個子系統的狀態矩陣用可估測標準式描述時，我們同樣利用李亞普諾夫漸近穩定理論分析估測誤差與系統輸出的收斂情形，推導並求解李亞普諾夫方程式後，我們能夠直接設計此系統的狀態估測器。除此之外，本論文尚且針對T-S模糊系統在考慮系統輸出收斂速度的要求下，進行控制器的設計與解決，並使系統輸出的響應收斂情形有大幅度的改善。

In the past, LMI（Linear Matrix Inequalities） technique is used to solve the fuzzy controller, observer and to analyze the stability of Lyapunov inequalities of the T-S (Takagi-Sugeno) fuzzy systems. However, there are still many difficulties in systematically designing the T-S fuzzy controller and the observer. In this thesis, we provide a fuzzy controller and observer design method for the nonlinear plant whose structure is represented by T-S fuzzy model. The model-based fuzzy controller and observer are designed by the concept of the so-called “PDC (Parallel Distributed Compensation)” [2]. Applying the Lyapunov asymptotic stability theorem instead of Lyapunov inequality, we can solve the Lyapunov equation via the algorithm provided in this work. The final stable controller and observer of the nonlinear plant can be obtained directly. This method is mainly based on the fact that each subsystem of T-S fuzzy model can be represented by the controllable and the observable canonical form. Besides, the decay rate of system state can also be improved.

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