國立中山大學,National Sun Yat-sen University,學位論文,thesis/dissertation,離散時間奇異系統的廣義H∞ 控制,Generalized H∞ Control for Discrete-Time Singular Systems

論文名稱 Title	離散時間奇異系統的廣義H∞ 控制 Generalized H∞ Control for Discrete-Time Singular Systems
系所名稱 Department	電機工程學系 Department of Electrical Engineering
畢業學年期 Year, semester	105 學年度第 2 學期 The spring semester of Academic Year 105	語文別 Language	中文 Chinese
學位類別 Degree	碩士 Master	頁數 Number of pages	44
研究生 Author	蘇晏瑩 Yen-yin Su
指導教授 Advisor	李立 Li Lee
召集委員 Convenor	高崇堯 Chung-Yao Kao
口試委員 Advisory Committee	葛世偉 shih wei kau
口試日期 Date of Exam	2017-07-24	繳交日期 Date of Submission	2017-09-01
關鍵字 Keywords	可容許的、線性矩陣不等式、性能指標、廣義H∞控制、離散奇異系統 generalized H∞ control, discrete singular system, performance measure, linear matrix inequality, admissible
統計 Statistics	本論文已被瀏覽 5673 次，被下載 21 次 The thesis/dissertation has been browsed 5673 times, has been downloaded 21 times.

中文摘要
在H∞控制問題上，通常會假設系統的初始條件為零，但實際上初始狀態往往是未知的。因上述問題，本論文針對離散時間奇異系統研究一種廣義型式的H∞控制。吾人藉由引進一種性能指標，稱為最壞情況時的範數，此性能指標可以反應出控制輸出如何被外在雜訊輸入和未知的初始條件影響，推導出離散時間奇異系統為可容許的，且其性能指標小於規範值的線性矩陣不等式條件。基於上述條件，我們可以推導出控制器存在的充分和必要條件，且讓閉迴路系統為可容許的，其性能指標小於某個規範值。最後，以數值模擬的例子來加以驗證論文提出的設計條件。
Abstract
In H∞ control problems, it is usually assumed that the system initial conditions are zero. In this thesis, a general type of H∞ control is investigated for discrete-time singular systems. With the introduction of a performance measure that is the worst-case norm of the regulated outputs over both exogenous inputs and initial conditions, linear matrix inequality sufficient and necessary criteria are obtained for discrete-time singular systems to be admissible and the performance measure to be less than a prescribed scalar. Based on the obtained results, necessary and sufficient conditions are derived for the existence of controllers that yield an admissible closed-loop system with its performance measure less than a prespecified value. Finally, numerical examples are given to demonstrate feasibility of the obtained results.

目次 Table of Contents
審定書………………………………………………………………… i 誌謝…………………………………………………………………… ii 中文摘要………………………………………………………….….. iii 英文摘要………………………………………………………….….. iv 圖次…………………………………………………………………… vi 符號說明………………………………………………………….….. vii 第一章序論………………………………………………………. 1 1.1文獻回顧與研究動機 ……………………………………….. 1 1.2論文綱要……………………………………………………... 2 第二章基本定義與性質…………………………………………. 3 第三章離散時間奇異系統的廣義分析……………………....... 5 3.1系統描述……………………………………………………... 5 3.2廣義分析…………………………………………………...... 6 第四章離散時間奇異系統的廣義設計……………………....... 15 4.1系統描述……………………………………………………... 15 4.2廣義設計…………………………………………………...... 16 4.3數值模擬……………………………………………………... 18 第五章離散時間奇異系統的強韌且廣義分析與設計…..…...… 23 5.1系統描述…………………………………………………….... 23 5.2強韌且廣義分析…………………………………………....... 23 5.3強韌且廣義設計…………………………………………....... 28 5.4數值模擬…………………………………………………….... 31 第六章結論………………………………………………………. 33 參考文獻 ……………………………………………………….……. 34

參考文獻 References
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