臺灣博碩士論文加值系統

本論文旨在探討時延系統之強健穩定度分析，強健穩定受到學者與專家注意與探討，在各型式之控制系統中皆可能遭遇時間延遲問題，時間延遲為不穩定的來源之一，因此控制系統的時間延遲強健穩定問題值得討論與研究。
時間延遲系統時常發生在訊息傳輸，如傳輸系統、通信系統、化學處理系統與動力系統都有延遲現象，在控制系統設計中含有限制性控制器時，致動器之動態範圍因飽和受到限制，故時延系統強健穩定飽和問題亦受到相當多的關注；本文應用Lyapunov-Krasovskii為基礎結合LMI(Linear Matrix Inequality)的方法，推導出延遲相關強健穩定準則，推導之結果與現有文獻比較，在相同例子下，可承受較大擾動之延遲時間範圍，最後，將所推出之準則應用於實例分析，確保系統在最大延遲時間範圍內仍保持漸近穩定。

This paper aims to explore robust stability analysis of time delay system. Robust stability for time delay system has been attracting the attention of many researchers. Time delay is frequently encountered in various control systems, and the existence of the delay is a source of instability. Therefore, the stability problem of time delay systems has been one of the most popular research areas in control systems over the years.
Time delay system is often occurring in the transmission of information or material between different parts of a system. Transportation systems, communication systems, chemical processing systems, and power systems are examples of time delay systems. In control system design, the limited power supply is the form of a saturating actuator in a practical system. In this thesis, one delay dependent robust stability criteria based on Lyapunov-Krasovskii functional combining with LMI approach has been developed and derived step by step. The proposed stabilization criteria is relatively simple to be checked by simulations and can be applied to the time delay systems with actuator saturation and perturbation. The given systems have been proven to be asymptotically stable.

摘要 I
Abstract II
目錄 III
圖目錄 V
表目錄 VI
第一章 緒論 1
1.1研究動機與目的 1
1.2 文獻探討 3
1.3 論文架構 4
第二章 相關數學理論與輔助定理 6
2.1 符號說明 6
2.2 相關數學理論與輔助定理 7
第三章 Lyapunov理論 11
3.1 穩定性研究與Lyapunov穩定 11
3.2 Lyapunov推導 13
3.3 Lyapunov-Krasovskii介紹 14
第四章 時延系統 16
4.1 時延系統介紹 16
4.2 時延無關與時延相關 16
4.3 輾壓系統之時延現象 17
第五章 問題與探討 21
5.1 前言 21
5.2 時延系統強健穩定準則 22
5.3 狀態回授控制器時延系統強健穩定準則 27
5.4 輸出回授控制器時延系統強健穩定準則 35
5.5 具飽和時延系統強健穩定準則 42
5.6 參數擾動穩定準則 50
5.6.1 參數擾動時延系統強健穩定準則 50
5.6.2 參數擾動狀態回授控制器時延系統強健穩定準則 54
5.6.3 參數擾動輸出回授控制器時延系統強健穩定準則 60
5.6.4 參數擾動具飽和時延系統強健穩定準則 65
5.7 實例探討 71
第六章 結論與未來研究方向 75
6.1 結論 75
6.2 未來研究方向 76
參考文獻 77

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