離散時間區間時延正向系統的穩定度分析與控制器設計

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：14

、訪客IP：3.145.95.233

姓名

張博竣(Bo-Jun Zhang) 查詢紙本館藏

畢業系所

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)

相關論文

★ 小型化 GSM/GPRS 行動通訊模組之研究	★ 語者辨識之研究
★ 應用投影法作受擾動奇異系統之強健性分析	★ 利用支撐向量機模型改善對立假設特徵函數之語者確認研究
★ 結合高斯混合超級向量與微分核函數之語者確認研究	★ 敏捷移動粒子群最佳化方法
★ 改良式粒子群方法之無失真影像預測編碼應用	★ 粒子群演算法應用於語者模型訓練與調適之研究
★ 粒子群演算法之語者確認系統	★ 改良式梅爾倒頻譜係數混合多種語音特徵之研究
★ 利用語者特定背景模型之語者確認系統	★ 智慧型遠端監控系統
★ 正向系統輸出回授之穩定度分析與控制器設計	★ 混合式區間搜索粒子群演算法
★ 基於深度神經網路的手勢辨識研究	★ 人體姿勢矯正項鍊配載影像辨識自動校準及手機接收警告系統

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

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

參考文獻

[1] O. Mason and R. Shorten, “The geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem,” Electronic Journal of Linear Algebra, vol. 12, pp. 42-63, 2005.
[2] X. Liu, L. Wang, W. Yu, and S. Zhong, “Constrained control of positive discrete-time systems with delays,” IEEE Transactions on Circuits and Systems Ⅱ, vol. 55, no. 2, pp. 193-197, 2008.
[3] M. Bus?owicz and T. Kaczorek, “Robust stability of positive discrete-time interval systems with time-delays,” Bulletin of The Polish Academy of Sciences: Technical Sciences, vol.52, no.2, 2004.
[4] Z. Shu, J. Lam, H. Gao, B. Du, and L. Wu, “Positive observers and dynamic output-feedback controllers for interval positive linear systems,” IEEE Transactions on Circuits and Systems Ⅰ, vol. 55, no. 10, pp. 3209-3222, Nov. 2008.
[5] M. A. Rami, F. Tadeo, and A. Benzaouia, “Control of constrained positive discrete systems,” Proceedings of 2007 American Control Conference, pp. 5851-5856, New York, USA, 2007.
[6] T. Kaczorek, “Stabilization of positive linear system by state-feedback,” Pomiary, Automatyka, Kontrola, vol. 3, pp. 2-5, 1999.
[7] M. A. Rami, and F. Tadeo, “Positive observation problem for linear discrete positive systems,” Proceeding of 45th IEEE Conference on Decision and Control, pp. 4729-4733, Athens, Greece, 2007.
[8] T. Kaczorek, “Stabilization of positive linear systems,” Proceedings of the 37th IEEE Conference on Decision and Control, pp. 620-621, 1998.
[9] M. A. Rami and F. Tadeo, “Controller synthesis for positive linear systems with bounded controls,” IEEE Transactions on Circuits and Systems Ⅱ, vol. 54, no. 2, pp. 151-155, 2007.
[10] J. Feng, J. Lam, P. Li, and Z. Shu, “Decay rate constrained stabilization of positive systems using static output feedback,” International Journal of Robust and Nonlinear Control, vol. 83, no. 3, pp. 575-584, 2010.
[11] X. Liu, “Stability analysis of switched positive systems: A switched linear copositive lyapunov function method,” IEEE Transactions on Circuits and Systems Ⅱ, vol. 56, no. 5, pp. 414-418, 2009.
[12] L. Benvenuti and L. Farina, “Eigenvalue regions for positive systems,” Systems & Control Letters, vol. 51, pp. 325-330, 2004.
[13] X. Liu, “Constrained control of positive systems with delays,” IEEE Transactions on Automatic Control, vol. 54, no. 7, pp. 1596-1600, 2009.
[14] P. D. Leenheer and D. Aeyels, “Stabilization of positive linear system,” Systems & Control Letters, vol. 44, no.4, pp. 259-271, 2001.
[15] J. Back and A. Astolfi, “Positive linear observers for positive linear systems: A Sylvester equation approach,” Proceeding of 2006 American Control Conference, pp. 4037-4042, Minneapolis, Minnesota, USA, 2006.
[16] F. Knorn, O. Mason, and R. Shorten, “On Linear Co-positive Lyapunov Functions for Sets of Linear Positive Systems,” Automatica, vol. 45, no. 8, pp. 1943-1947, 2009.
[17] L. Caccetta, L. R. Foulds, and V. G. Rumchev, “A positive linear discrete-time model of capacity planning and its controllability properties,” Mathematical and Computer Modelling, vol. 40, no. 1-2, pp. 217-226, 2004.
[18] H. Gao, J. Lam, C. Wang, and S. Xu, “Control for stability and positivity: Equivalent conditions and computation,” IEEE Transactions on Circuits and Systems Ⅱ, vol. 52, no. 9, pp. 540-544, Sep. 2005.
[19] M. A. Rami, F. Tadeo, and A. Benzaouia, “Control of constrained positive discrete systems,” Proceeding of 2007 American Control Conference, pp. 5851-5856, New York, USA, 2007.
[20] P. Ling, J. Lam, and Z. Shu, “Positive observers for Positive interval linear discrete-time delay systems,” Proceedings of 48th IEEE Conference on Decision Control, pp. 6107-6112, Shanghai, P.R., China, 2009.
[21] B. Roszak and E. J. Davison, “Necessary and sufficient conditions for stabilizability of positive LTI systems,” Systems & Control Letters, vol. 58, pp. 474-481, 2009.
[22] O. Mason and R. Shorten, “Quadratic and copositive Lyapunov functions and the stability of positive switched linear systems,” Proceedings of 2007 American Control Conference, pp. 657-662, 2007.
[23] O. Mason and R. Shorten, “On linear copositive Lyapunov functions and the stability of switched positive linear systems,” IEEE Transactions on Automatic Control, vol. 52, no. 7, pp. 1346-1349, 2007.
[24] M. A. Rami, and F. Tadeo, “Positive observation problem for linear discrete positive systems,” Proceedings of 45th IEEE Conference on Decision and Control, pp. 4729-4733, Athens, Greece, 2007.
[25] O. Mason and R. Shorten, “Some results on the stability of positive switched linear systems,” Proceedings of 43rd Conference on Decision and Control, 2004, pp. 4601-4606.
[26] N. Dautrebande and G. Bastin, “Positive linear observers for positive linear systems,” Proceeding of 1999 Europe Control Conference, 1999.
[27] Abraham Berman, Robert J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, 1994, SIAM. ISBN 0-89871-321-8.
[28] A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, 1979 (chapter 2), ISBN 0-12-092250-9
[29] R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, 1990 (chapter 8).
[30] Krasnosel′skii, M. A.; Lifshits, Je.A.; Sobolev, A.V. (1990). Positive Linear Systems: The method of positive operators. Sigma Series in Applied Mathematics. 5. Berlin: Helderman Verlag. pp. 354 pp.
[31] Henryk Minc, Nonnegative matrices, John Wiley&Sons, New York, 1988, ISBN 0-471-83966-3
[32] Seneta, E. Non-negative matrices and Markov chains. 2nd rev. ed., 1981, XVI, 288 p., Softcover Springer Series in Statistics. (Originally published by Allen & Unwin Ltd., London, 1973) ISBN 978-0-387-29765-1
[33] J. E. Slotine and W. Li, Applied Nonlinear Control, Englewood Cliffs, NJ: Prentice-Hall, Inc., 1991.
[34] H. K. Khalil, Nonlinear Systems, third ed., Upper Saddle River, NJ: Prentice-Hall, Inc., 2002.
[35] M. Vidyasagar, Nonlinear Systems Analysis, New Jersey: Prentice-Hall, Inc., 2000.
[36] L. Farina and S. Rinaldi, Positive Linear System: Theory and Application, NewYork: Wiley, 2000.
[37] M. Buslowitz and T. Kaczorek, Reachability of positive discrete-time
with one time-delay, in National Conf. on Automation of Discrete
Processes, Zakopane, 2004 (in Polish).
[38] M. Buslowitz and T. Kaczorek, Robust stability of positive discretetime
interval systems with time-delays, Bulletin of the Polish Academy
of Sciences, Technical Sciences, vol. 52, no. 2, 2004, pp. 99–102.
[39] T. Kaczorek, Stability of positive discrete-time systems with timedelay,
in 12th Mediterranean Conf. on Control and Automation,
Kasadasi, Turkey, 2004.
[40] Abdelaziz Hmamed, Abdellah Benzaouia, Mustapha Ait Rami and Fernando Tadeo, Positive stabilization of discrete-time systems with unknown delay and bounded controls, Proceedings of the European Control Conference 2007 Kos, Greece, July 2-5, 2007
[41] Krebs CJ (2001) Ecology: the experimental analysis of distribution and abundance (5th edition). San Francisco. Benjamin Cummings.
[42] Charlesworth, B. (1980) Evolution in age-structured population. Cambridge.
[43] Lotka, A.J. (1956) Elements of mathematical biology. New York. Dover Publications Inc.
[44] Kot, M. (2001) Elements of Mathematical Ecology, Cambridge. Cambridge University Press.
[45] Leslie, P.H. (1945) "The use of matrices in certain population mathematics". Biometrika, 33(3), 183–212.
[46] Leslie, P.H. (1948) "Some further notes on the use of matrices in population mathematics". Biometrika, 35(3–4), 213–245.

指導教授

莊堯棠(Yau-Tarng Juang)

審核日期

2018-7-25

推文