臺灣博碩士論文加值系統

本研究使用切換系統文獻理論，對連續時T-S模糊控制系統的穩定性分析，做出更為明確的穩定性討論。
T-S 模糊控制系統穩定性文獻中，已有利用模糊分割與模糊規則庫，使子系統矩陣間存在二次的共同正定 矩陣的條件較不嚴苛。透過模糊分割可以將T-S 模糊控制系統分割成數個系統群，群內各系統間計算共同 矩陣可以較容易得到穩定性的結果。基本上，本論文承襲這樣的論點，針對2階系統，使用最糟切換法則、Joint spectral radius 的技巧來改進現有文獻中，當群組內二次的共同正定 矩陣無法得到，便無法得到穩定性結論的結果。依模糊規則庫而行的切換軌跡，是否連結成最糟切換路徑，對於判斷系統是否穩定具有相當大的助益。
Joint spectral radius 的技巧可適用於任何階數的系統矩陣，對於穩定性的分析較不具限制性，不過它的計算非常煩雜。本論文提出Joint spectral radius技巧的著眼點，在於它在離散時切換系統穩定性分析伴演著關鍵的角色。若各系統停留時間已知，切換次序不明的情形下，相較於尋找共同 矩陣的分析法，Joint spectral radius技巧能對連續時T-S模糊控制系統的穩定性分析獲致較不保守的結論。

Investigated in this thesis, is a stability analysis for T-S fuzzy control systems using switched systems theory, which leads to more conclusive results.
In the T-S fuzzy model stability literature, structural information of the fuzzy rules were intelligently incorporated to develop the concept of the maximal overlapped-ruled groups (MORG) to achieve a sufficient condition for stability, which was much less conservative compared with earlier ones. In each of such groups, the task of finding a common quadratic Lyapunov function is much simplified. However, when the search of a common positive definite P matrix failed, stability analysis is inconclusive. In that regard, for second-order systems, we use the concepts of worst case switching law and joint spectral radius adopted from switched-system stability analysis to reduce the conservatism of existing methods.
Despite the inherent difficulty of computation, the concept of joint spectral radius is also applicable to the analysis of higher-order discrete-time switched systems. In view of the fact that the determination of stability requires only the knowledge of joint spectral radius being less than 1, rather than the exact number of joint spectral radius, we consider efforts to estimate joint spectral radius worthwhile. When the dwelling time for each subsystem is known, joint spectral radius can be used in the stability analysis of continuous-time switched system, and are more likely to lead to a conclusion than current quadratic Lyapunov function based methods.

摘要 Ⅴ
英文摘要 Ⅵ
目次 Ⅶ
圖目錄 Ⅸ
第一章 緒論 1
1.1 研究動機與目的 1
1.2 研究背景 2
1.3 研究方法 4
1.4 內容架構 6
第二章 模糊系統概要 7
2.1 模糊邏輯控制器 7
2.1.1 模糊控制概要 7
2.2.2 模糊化 9
2.2.2 知識庫 10
2.2.3 模糊決策邏輯 11
2.2.4 解模糊化 12
2.2.4 T-S 模糊系統 13
2.2 MORG理論 15
2.2.4 MORG概要 15
2.2.4 MORG定義 15
2.2.5 MORG穩定性解析 19
2.3 MORG群組結果 21
第三章 最糟切換路徑 25
3.1 Lyapunov function 25
3.2 最糟切換的計算 32
3.2.1 系統軌跡順逆判斷式 33

3.2.2 最糟切換群組分配 38
第四章 Joint spectral radius 39
4.1 範數(Norm) 39
4.1.1 向量範數 39
4.1.2 矩陣範數 40
4.1.3 Spectral radius 41
4.2 Joint spectral radius定義 42
4.2.1 Joint spectral radius上下邊界 43
4.2.2 kronecker lifting 45
4.2.3 Semidefinite lifting 47
4.2.4 Ellipsoid norm approximation 48
第五章 研究分析與討論 49
5.1 研究成果 49
5.2 延伸研究成果 56
5.2.1 延伸研究成果一 56
5.2.2 延伸研究成果二 59
第六章 結論 62
參考文獻 63

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