摘 要
本文中旨在探討近年來時延系統穩定度的強健控制系統分析，經由定理推導與例題模擬，並且求得系統可以達到漸近穩定所能容忍之最大延遲時間大小。文中引用李亞普諾夫函數Lyapunov-Krasovskii、李亞普諾夫方程式(Lyapunov equation)、與線性矩陣不等式(Linear Matrix Inequality：LMI)來研究時延系統之強健穩定分析。經由本文所得之定理求得此系統最大的時延範圍仍使系統為強健穩定，本文中以水質監控系統、熱交換控制系統與電子電路控制系統之實例討論，在控制系統能承受的最大時間延遲時間範圍內，使得系統仍能漸近穩定。

關鍵詞：李亞普諾夫函數，線性矩陣不等式，時間延遲，
延遲微分系統

Abstract
Some discussions have been made with the same examples that appear in many recent papers via illustrative examples. A neutral system with distributed time-delay is asymptotically stable. In this thesis, The control system applied the properties of the Lyapunov equation, Lyapunov -Krasovskiiand, linear matrix inequality(LMI), Newton-Leibniz formula and model transformation. These properties are employed to investigate the robust stabilization conditions. This thesis shows a maximum delay bound is derived for the robust stabilization of time-delay control systems. This thesis shows examples that the Physics mean a control system of time-delay, including Stream Water Quality, Electrical-circuit Models and Heat Exchanger Dynamics. The control system can maximum the allowable delay bound to a greater degree than the memoryless state feedback via illustrative examples. A system with distributed delay is asymptotically stable.

Keyword : Lyapunov function, Linear Matrix Inequality(LMI),
Time-delay, Neutral system.

目 錄
頁碼
中文摘要 Ⅰ
英文摘要 Ⅱ
目錄 Ⅲ
圖目錄 Ⅴ
表目錄 Ⅵ
第一章 緒論 1
1-1 研究動機 1
1-2 研究背景 1
1-3 文獻探討 2
1-4 章節組織 3
第二章 相關數學理論與輔助定理 5
2-1 符號說明 5
2-2 相關數學理論與輔助定理 5
第三章 水質監控控制系統 7
3-1 水質監控系統介紹 7
3-2 水質監控系統－Newton-Leibniz formula 8
3-3 水質監控系統－Model transformation 17
3-4 水質監控系統－例題模擬 25
3-5 結語 31
第四章 熱交換控制系統 32
4-1 熱交換控制系統介紹 32
4-2 熱交換控制系統－Newton-Leibniz formula 33
4-3 熱交換控制系統－Model transformation 37
4-4 熱交換控制系統－例題模擬 41
4-5 結語 46
第五章 電子電路控制系統 47
5-1 電子電路控制系統介紹 47
5-2 電子電路控制系統－Model transformation 51
5-3 電子電路控制系統－例題模擬 55
5-4 結語 58
第六章 結論與建議 59
6-1 結論 59
6-2 未來研究方向與建議 59
參考文獻 61

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