在本文?堶控艦峇F一種新的技巧結合算子理論來分析線性時變系統，這使得我們可以把線性時變系統的強韌控制問題做全面且簡單的處理，更可以使用此方法把非時變系統採用到時變的例子?堶情C首先構造此方法所需用的算子，然後應用到線性時變系統，接著更應用到強韌控制的結構化奇異值問題，其結果跟線性非時變系統相似，接著建構標準 控制問題，並採用線性矩陣不等式的方法求得次最佳控制器來滿足系統所需要的性能，最後利用數值方法來加以討論。

In this paper we adopt a new technique combined with operator theorem to analysis linear time-varying system. This make us solve the robust control problems of linear time-varying system more easily. Also, we can apply this method to the problems of linear time-invarying system. First, we construct the operator we want to use, then apply it to the linear time-varying system. Moreover, we can apply this method to the structure singular value problem of robust control, and the result is similar with the linear time-invarying system. Then , we construct the standard control problem , and adopt linear matrix in- equality to get suboptimal controller to satisfy the robust performance we need. Finally,we use numerical method to discuss it.

目錄…………………………………………………… I
圖索引………………………………………………… IV
符號說明……………………………………………… VI
論文摘要(中文)………………………………………VII
論文摘要(英文)…………………………………… VIII
第一章緒論………………………………………………1
1.1 前言 ……………………………………………… 1
1.2 文獻回顧………………………………………… 2
1.3 研究動機和目的………………………………… 4
1.4 文章架構………………………………………… 5
第二章 預備數學理論……………………………… 6
2.1 各類算子…………………………………… 6
2.1.1 單邊偏移算子……………………… 6
2.1.2 方塊對角化算子…………………… 6
2.2 基本定理……………………………………………………… 10
第三章 線性時變系統………………………………… 12
3.1 時變系統和穩定度的描述………………… 12
3.2 系統函數…………………………………… 13
3.3 歸納範數的評估…………………………… 17
第四章 線性時變系統的 分析…………………………20
4.1 線性分式轉換……………………………… 21
4.2 結構化奇異值……………………………… 23
第五章 線性時變系統的 控制問題………………… 26
5.1 線性矩陣不等式…………………………… 27
5.2 標準的 控制問題…………………………… 29
5.3 將線性矩陣不等式的方法用於次最佳 控制 32
5.3.1 有用的結果………………………… 33
5.3.2 建構次最佳 控制問題……………… 34
5.3.3 線性矩陣不等式公式和凸論性質……42
5.3.4 結果討論與分析…………………… 45
第六章 週期系統和有限維條件 ………………………47
6.1 第一個條件………………………………… 47
6.2 第二個條件………………………………… 47
6.3 結果討論…………………………………… 51
第七章 數值解法與討論……………………………… 52
7.1 流程介紹…………………………………… 52
7.1.1 遞迴解法…………………………… 52
7.1.2 聯立解法…………………………… 55
7.2 數值例子…………………………………… 56
7.2.1遞迴數值例子………………………… 56
7.2.2 聯立數值例子……………………… 59
7.3 結果討論…………………………………… 61
7.4 未來展望…………………………………… 63
參考文獻……………………………………………… 64
附錄………………………………………………………90

圖索引
圖4-1 下側線性分式轉換………………………………68
圖4-2 上側線性分式轉換………………………………68
圖4-3 系統函數變成線性分式轉換……………………69
圖5-1 閉迴路系統………………………………………69
圖5-2 R和S滿足定理5.6的流程圖……………………70
圖5-3 求得 控制器的流程圖………………………… 71
圖5-4 遞迴解法的程式流程圖…………………………72
圖5-5 聯立解法的程式流程圖…………………………73
圖7-1 週期時變受控系統的X變化圖………………… 74
圖7-2 週期時變受控系統的Z變化圖………………… 75
圖7-3 週期時變閉迴路系統的X變化圖……………… 76
圖7-4 週期時變閉迴路系統的Z變化圖……………… 77
圖7-5 週期時變系統控制器狀態空間變化圖…………78
圖7-6 一般時變受控系統的X變化圖………………… 79
圖7-7 一般時變受控系統的Z變化圖………………… 80
圖7-8 一般時變閉迴路系統的X變化圖……………… 81
圖7-9 一般時變閉迴路系統的Z變化圖……………… 82
圖7-10 一般時變系統控制器狀態空間變化圖……… 83
圖7-11 一般時變受控系統的X變化圖…………………84
圖7-12 一般時變受控系統的Z變化圖…………………85
圖7-13 一般時變閉迴路系統的X變化圖………………86
圖7-14 一般時變閉迴路系統的Z變化圖………………87
圖7-15 一般時變系統控制器狀態空間變化圖……… 88
圖7-16 線性時變系統………………………………… 89

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