在許多文獻中，處理非線性系統問題通常都是利用描述成Takagi-Sugeno (T-S) 模糊模組的型式來做探討。模糊控制器設計方法大多採用平行分配補償 (Parallel Distributed Compensation - PDC) 之設計觀念並使用里阿伯諾 (Lyapunov) 穩定法則來做此類系統的穩定性分析。不過，當T-S 模糊系統所包含大量的模糊規則數，轉換後的LMI 總數目也急劇增加。在此情況下，找到一個共同正定矩陣來滿足系統之穩定條件是很難的，也導致LMI 演算法之無解機率大幅提高。由於上述的困難點，以及問題的癥結所在，於是本計畫嘗試在模糊區域系統上處理非線性系統之穩定性問題。本計畫之一個議題是想使用模糊區域概念設計模糊控制器，並結合分段式里阿伯諾(Lyapunov)穩定準則來達成時延系統及∞ H 控制的性能。另外一個焦點是討論時變的T-S 模糊系統的穩定度,最後利用混合型的特徵值來取代混合型的權重，透過根軌跡的作圖和強健控制理論的觀念即可判斷T-S 模糊系統的穩定度,且其穩定度的判斷比傳統二次式Lyapunov 函數較容易處理與求解。因此，本計畫利用分段里阿伯諾穩定準則只需求出各模糊區域裡的個別正定矩陣，及利用古典控制法則加入模糊系統分析，如此便可使判定方法的保守性降低。本計畫提出的控制準則預期可以簡單的想法、清楚的數學推導處理模糊區域之穩定性問題。 ; Nonlinear systems have commonly been described by Takagi-Sugeno (T-S) fuzzy model in many literatures. Parallel Distributed Compensation (PDC) is a popular concept to design a T-S fuzzy controller, and Lyapunov criterion is a familiar method to analyze its stability. However, these Linear Matrix Inequalities (LMIs) are greatly increased if the T-S fuzzy model contains lots of plant rules. It is difficult to find a common Lyapunov matrix to satisfy the stability condition of a system. The problems aforementioned are some of the problems we have to handle. This project deals with various stability criterions in the T-S fuzzy region system. One issue of our projects is to utilize the fuzzy region concept to design a new fuzzy controller with time delay system and ∞ H performance derived from the piecewise Lyapunov stability criterion. Another focuse is to explore the stability of a time-varying system. At last, another approach is proposed to search for eigenvalues of T-S fuzzy model in any mixed weighting cases. This systematic method is developed by the technique of root locus and the robust control theorem to determine the stability of a T-S fuzzy system. The Lyapunov matrix P is a sufficient condition but not a necessary condition for the stability of T-S fuzzy systems. Hence, an effective way will be explored to ensure the stability of the system. It is found that the proposed conditions are less conservative than those of past works. This project tackles the problem of a state feedback fuzzy regional control with a simple idea and clear mathematical derivations. ; 研究期間 9808 ~ 9907
