在 H∞ 控制問題中，通常考慮的受控體是零初始值的系統。而本論文藉著考慮非零初始值的正常狀態空間系統之現有文獻，將之推廣到奇異時變系統，並定義了有限時間的廣義性能指標。吾人以矩陣不等式的處理技巧推導出一組與奇異時變系統是無脈衝的且其廣義性能指標小於給定的定值若且唯若的矩陣不等式結果。接著考慮兩種常見的狀態回授控制器使所設計的閉迴路奇異時變系統無脈衝且具有良好的抗干擾效果。

In H∞ control problem, it is usually assumed that the system initial conditions are zero. This thesis extends the results of H∞ control for state-space time-varying systems with nonzero initial conditions to singular time-varying systems, meanwhile redefines the generalized performance index for the considered systems. Necessary and sufficient conditions in the form of linear matrix equality and inequality are derived for singular time-varying systems possessing simultaneously the impulse-free property and the above-mentioned performance measure is less than a pre-specified value. Two kinds of commonly used state feedback controllers are also considered to make the closed-loop singular systems performance specification.

摘要.................................................................i
符號表...............................................................v
第一章 緒論.........................................................1
1-1節背景與動機...............................................1
1-2節論文架構.................................................2
第二章 幾個矩陣性質.................................................3
第三章 線性時變奇異系統的廣義 H∞ 分析...............................4
3-1節系統描述與性質...........................................4
3-2節廣義 H∞ 性能指標定義與問題描述..........................6
3-3節奇異系統之廣義 H∞ 分析..................................10
第四章 奇異時變系統之廣義 H∞ 控制器設計...........................26
4-1節系統描述................................................26
4-2節兩種狀態控制器設計......................................26
第五章 結論........................................................33
參考文獻............................................................34

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