臺灣博碩士論文加值系統

本論文係針對廣義的李普諾夫方程式，分別提出其解存在及解唯一之充份必要條件。此外吾人亦推導出保證廣義李普諾夫方程式對於參數靈敏度存在且唯一之充份必要條件。最後，吾人將以一些範例來說明主要定理。

In this thesis, the generalized Lyapunov equation is reconsidered. Both of the necessary and sufficient conditions for the solution existence and solution uniqueness of such generalized Lyapunov equation are investigated. Moreover, the necessary and sufficient conditions for the uniqueness of solution sensitivity with respect to parameter’s variation is developed. Finally, some numerical examples are provided to illustrate the use of the main results.

中文摘要…………………………………………………………………I
英文摘要………………………………………………………………...II
致謝……………………………………………………………………..IV
目錄…………………………………………………………………….. V
第一章 介紹…………………………………………………………1
第一節 概論…………………………………………………………1
第二節 符號…………………………………………………………2
第二章 定義與定理…………………………………………………4
2-1 歸納矩陣範數………………………………………………4
2-2 矩陣運算子…………………………………………………8
2-3 矩陣的導數………………………………………………..17
第三章 連續時間系統的廣義李普諾夫方程式…………………..22
第四章 離散時間系統的廣義李普諾夫方程式…………………..39
第五章 結論與未來研究方向……………………………………..55
5-1 結論………………………………………………………..55
5-2 未來研究方向……………………………………………..55
參考文獻………………………………………………………………..57

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