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 總數目也急遽增加。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。依照上述的困難點，吾人瞭解問題的癥結所在，於是本計畫嘗試處理非線性系統之穩定性問題呈現於模糊區域系統 (Fuzzy Region System)上。本計畫第一個方向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∞ H 控制性能。另外一個方面討論離散的T-S 模糊系統的穩定度,利用混合型的特徵值來取代混合型的權重，透過根軌跡的作圖觀念及Jury test 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得。於此，本計畫利用分段里阿伯諾穩定準則只需求出各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成功地以簡單的想法、清楚的數學推導處理模糊區域之穩定性問題。 ; Nonlinear systems have been described by Takagi-Sugeno (T-S) fuzzy model in many literatures. Parallel Distributed Compensation (PDC) is a popular concept to design 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 achieve system stability. 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 of our projects utilizes the fuzzy region concept to design a new fuzzy controller with ∞ H performance derived from the piecewise Lyapunov stability criterion. In addition, another approach is proposed to search for eigenvalues of T-S fuzzy model in any mixed weighting cases. This systematic method is developed by well-known Jury’s test and the root locus to determine the stability. Furthermore the root locus is also able to realize the transient response for a T-S fuzzy model. 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. Therefore, the proposed conditions are less conservative than 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 9708 ~ 9807
