間隙度量是一種不同於範數度量的系統量測概念，有著較廣泛而直觀的優點。本論文的目的，便是在探討由間隙度量概念所設計的控制器與目前較受廣泛應用的 強韌穩定控制器，其相互之間的關係。並對於間隙度量在線性非時變系統上的各種性質加以討論。
由間隙度量的強韌穩定條件與計算式子的推導，我們得到由間隙度量所求得的控制器與 強韌穩定控制器具有完全相同的穩定邊限。不過，由於 強韌穩定控制器有著較佳的計算工具，因此可以得到較低階控制器。另外，在ν-間隙度量的迴路成型控制器設計方面，由ν-間隙度量的幾何意義來看，Vinnicombe所提出的迴路成型設計步驟，在實際應用上難以求得理想的控制器。
在間隙度量的性質方面，我們探討由文獻[H,S]中所提出的間隙度量保守性質，並提出一些可用來輔助設計控制系統的間隙度量性質。

In this paper, the gap metric is introduced to study the robustness of the stability of feedback systems. A relation between the gap metric and coprime fractions is also investigated.
It is shown that the stability radius of the controller in the gap metric is equal to the stability margin of the controller. In the loop-shaping design procedure in the ν-gap metric, it is practically hard to formulate an ideal controller. Finally, this paper studied the conservatism of the gap metric, and proposed some properties that can help for control design and analysis.

目錄 Ⅰ
圖索引 Ⅴ
論文摘要（中文） Ⅶ
論文摘要（英文） Ⅷ
符號表 Ⅸ
第一章 緒論 1
1.1. 前言 1
1.2. 研究動機 2
1.3. 文獻回顧 3
1.4. 文章架構 5
第二章 間隙度量 7
2.1. 間隙度量 7
2.1.1. 兩子空間的間隙 7
2.1.2. 兩閉運算子的間隙 8
2.1.3. 有向間隙值的計算 9
2.2. 間隙拓樸 12
2.2.1. 圖形拓樸(Graph topology) 12
2.2.2. 間隙拓樸(gap topology) 13
2.3. 其他的度量形式 13
2.3.1. 圖形度量(Graph metric) 13
2.3.2. 互質分解之H∞範數度量 14
2.3.3. T-間隙度量 15
2.3.4. Pointwise-間隙度量 15
2.3.5. ν-間隙度量 16
第三章 間隙度量控制器的設計 18
3.1. 可穩定性(STABILIZABILITY) 18
3.2. 間隙度量控制器設計 19
3.2.1. 強韌穩定條件 19
3.2.2. 控制器設計 20
3.2.3. 實例驗證 25
3.3. 間隙度量控制器的強韌性 29
第四章 -間隙度量 35
4.1. -間隙度量定義 35
4.2. -間隙度量的幾何意義 38
4.3. -間隙度量的強韌性質 41
第五章 圖形拓樸之迴路成型設計 44
5.1. 迴路成型(LOOP SHAPING) 44
5.2. H∞迴路成型控制器的設計 48
5.3. 間隙度量迴路成型控制器設計 50
5.4. -間隙度量迴路成型控制器設計 51
5.5. 實例設計與比較 52
5.5.1. H∞迴路成型的設計 57
5.5.2. 間隙度量之迴路成型的設計 59
5.5.3. ν-間隙度量之迴路成型的設計 60
5.5.4. 比較與討論 65
第六章 間隙度量其他性質的探討 66
6.1. 間隙度量保守性質的討論 66
6.1.1. 間隙度量的保守性質 66
6.1.1.1. 零點在虛軸上的間隙度量值 67
6.1.1.2. 極點在虛軸上的間隙度量值 69
6.1.2. 討論 70
6.1.2.1. 零點在虛軸上 70
6.1.2.2. 極點在虛軸上 73
6.2. 系統性能與間隙度量 73
6.3. 間隙度量與系統極點 77
第七章 結論與未來展望 80
7.1. 結論 80
7.2. 未來展望 82
參考文獻 83

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