離散時間區間時延正向系統的穩定度分析與控制器設計

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姓名

張博竣(Bo-Jun Zhang) 查詢紙本館藏

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電機工程學系

論文名稱

離散時間區間時延正向系統的穩定度分析與控制器設計
(Stability Analysis and Controller Design for Discrete-time Interval Positive Systems with Delay)

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摘要(中)

本論文係研究區間時延正向系統之穩定性分析及穩定化控制器設計，研究的範疇為離散時間的系統，系統中含有的區間以及延遲時間為不確定量的因子，是本文主要探討的部分。針對正向性與穩定性分析問題，而推導出新的充分和必要條件。接著利用前述分析的結果，配合線性規劃的方法來設計狀態迴授控制器。最後以實際的Leslie系統為例，討論補償前與補償後系統性能的差異，經由模擬的結果顯示，所設計的控制器是有效且適用的。

摘要(英)

This thesis is concerned with stability analysis and controller design of interval positive systems with delay. The research scope is discrete-time systems. The interval and delay time contained in the system are the factors of uncertainty. For the problems of positiveness and stability analysis, we derive some new sufficient and necessary conditions. Based on these conditions, the design of the controllers with the state feedback can be applied to the stabilization design of the control system. Using the results of the foregoing analysis, the parameters of the controllers are sought in conjunction with the linear programming method. Finally, taking the actual discrete-time interval positive system with delay as an example. The simulation results,show that the designed controllers are effective and applicable.

關鍵字(中)

★ 正向系統

關鍵字(英)

★ Positive Systems

論文目次

目錄
摘要.................................................I
Abstract...............................................II
致謝...............................................III
目錄................................................IV
圖目錄...............................................VI
第一章緒論.............................................1
1.1 研究動機與研究目標...................................1
1.2 論文架構............................................2
第二章符號與介紹........................................3
2.1 符號................................................3
2.2 方塊矩陣............................................3
2.3 非負矩陣............................................3
2.4 離散時間正向系統.....................................4
2.5 離散時間時延正向系統.................................4
2.6 Lyapunov’s Direct Method...........................5
2.7 漸近穩定............................................7
2.8 線性規劃............................................7
2.9 結論................................................8
第三章離散時間區間時延正向系統之穩定度分析................9
3.1離散時間區間時延正向系統之穩定度分析....................9
3.2 舉例說明............................................14
3.3 結論...............................................17
第四章離散時間區間時延正向系統之控制器設計...............18
4.1 離散時間正向區間時延系統之控制器設計..................18
4.2 舉例說明...........................................25
4.3 結論..............................................30
第五章 Leslie系統的穩定性問題...........................31
5.1 Leslie矩陣的概述...................................31
5.2 Leslie系統的概述...................................31
5.3 Leslie系統的穩定性.................................32
5.4 結論..............................................36
第六章總結與未來展望...................................37
參考文獻...............................................38
附錄...................................................45

圖目錄
圖3.1系統狀態響應(3.21).................................................16
圖3.2系統狀態響應(3.22) .......................................................16
圖4.1 x_1 (k)的狀態應.....................................................28
圖4.2 x_2 (k)的狀態響應.....................................................29
圖4.3 x_3 (k)的狀態響應.....................................................29
圖5.1 x_1 (k)之狀態響應.....................................................34
圖5.2 x_2 (k)之狀態響應.....................................................35
圖5.3 x_3 (k)之狀態響應.....................................................35

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指導教授

莊堯棠(Yau-Tarng Juang)

審核日期

2018-7-25

推文