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研究生:郭志宏
研究生(外文):Chih-Hung Kuo
論文名稱:描述系統根叢集於廣義線性矩陣不等式區域之強健性分析
論文名稱(外文):Robust Pole-Clustering in Generalized LMI Regions Analysis for Descriptor Systems
指導教授:李立李立引用關係
指導教授(外文):Li Lee
學位類別:碩士
校院名稱:國立中山大學
系所名稱:電機工程學系研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:50
中文關鍵詞:廣義線性矩陣不等式區域描述系統強健根叢集
外文關鍵詞:descriptor systemsgeneralized LMI regionsrobust pole clustering
相關次數:
  • 被引用被引用:2
  • 點閱點閱:122
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  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0

本論文擬以線性矩陣不等式為工具來探討描述系統之根叢集判定問題;我們推導出一充分且必要的線性矩陣不等式條件來同時判別一個描述系統的正規性、脈衝免疫性及有限特徵值落於廣義線性矩陣不等式區域內。由於一般控制系統皆具有不確定量的存在,因此,我們對二種不確定量,即範數有界和凸多邊形不確定量,分別提出充分條件來保證不確定描述系統的強健根叢集特性。最後,我們提出以線性矩陣不等式為基礎的狀態迴授控制器設計法則,並提出數個範例之模擬結果以說明前述理論之正確性和可行性。


In this thesis, an LMI-based pole-clustering characterization for descriptor systems is investigated. A necessary and sufficient condition for checking simultaneously the regularity, impulse immunity, and finite eigenvalues locating in the generalized LMI regions is derived. Since uncertainty exists inevitably in control systems, we propose two sufficient conditions to guarantee the robust pole clustering in the generalized LMI regions for uncertain descriptor systems with two types of uncertainties, i.e. the norm bounded uncertainty and the convex polytopic uncertainty. The LMI-based state feedback controller design methods are developed as well. Finally, the validity and the feasibility of our theoretical results are verified by the numerical simulation results of several examples.


摘要i
符號表iv
第一章 序論1
  1-1 節 文獻回顧與研究動機1
  1-2 節 論文綱要3
第二章 描述系統之根叢集分析4
  2-1 節 系統基本性質與數學基礎4
  2-2 節 廣義線性矩陣不等式區域- 區域 6
  2-3 節 根叢集於 區域之分析 9
第三章 描述系統之強健根叢集分析16
  3-1 節 問題描述16
  3-2 節 具範數有界不確定量之強健根叢集於 區域之分析 18
  3-3 節 具凸多邊形不確定量之強健根叢集於 區域之分析 24
第四章 控制器設計與數值模擬29
  4-1 節 狀態迴授控制器設計29
  4-2 節 數值模擬33
第五章 結論47
參考文獻48


[1] L. Dai, Singular Control Systems, Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1989.[2] F. L. Lewis, “A survey of linear singular systems,” Circuits, Systems, and Sig. Proc., vol. 5, no. 1, pp. 3-36, 1986.[3] G. C. Verghese, B. C. Levy, and T. Kailath, “A generalized state-space for singular systems,” IEEE Trans. Automatic Control, vol. 26, pp. 811-831, 1981.[4] J. D. Cobb, “Controllability, observability, and duality in singular systems,” IEEE Trans. Automatic Control, vol. 29, pp. 1076-1082, 1984[5] D. J. Bender and A. J. Laub, “The linear-quadratic optimal regulator for descriptor systems,” IEEE Trans. Automatic Control, vol. 32, no. 8, pp. 672-688, 1987.[6] M. Chilali, and P. Gahinet, “ design with pole placement constraints: an LMI approach,“ IEEE Trans. Automatic Control, vol. 41, no. 3, pp. 358-367, 1996.[7] M. Chilali, P. Gahinet, and P. Apkrian, “Robust pole placement in LMI regions,” IEEE Trans. Automatic control, vol. 44, no. 12, pp. 2257-2270, 1999[8] D. Peaucelle, D. Arzelier, O. Bachelier, and J. Bernussou, “A new robust D-stability condition for real convex polytopic uncertainty,” Systems & Control Letters, vol. 40, pp. 21-30, 2000.[9] C. H. Fang, W. R. Horng, and L. Lee, “Pole-clustering inside a disk for generalized state-space systems-an LMI approach,” Proc. 13th IFAC, San Francisco, CA, vol. G, pp. 209-214, 1996.[10] K. L. Hsiung and L. Lee, “Pole-clustering characterization via LMI for descriptor systems,” Proc. of the 36th CDC, pp. 1313-1314, 1997.[11] K. L. Hsiung, “Pole-clustering analysis and design for descriptor systems: An LIM approach,” Master dissertation, National Sun Yat-Sen university, Taiwan, Republic of China, 1997.[12] J. L. Chen, L. Lee, and C. H. Fang, “Robust pole clustering in LMI regions for descriptor systems with parametric uncertainty,” Proc. of 1999 R.O.C. Automatic Control Conference, pp. 384-389, 1999[13] J. L. Chen and L. Lee, “Robust pole clustering for descriptor systems with norm-bounded uncertainty,” Proc. of 2001 ACC, pp. 2953-2954[14] K. L. Hsiung and L. Lee, “Lyapunov inequality and bounded real lemma for discrete-time descriptor systems,” IEE Proc. Control Theory Appl., vol. 146, no. 4, pp. 327-331, 1999.[15] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in systems and Control Theory, vol. 15. Philadelphia: SIAM, 1994.[16] C. H. Fang, L. Hong, S. W. Kau and L. Lee, “An LMI approach for robust stability of continuous-time descriptor systems families,” Proc. of 2002 R.O.C. Automatic Control Conference, pp.203-207, 2002.[17] C. H. Fang, L. Lee, and A. Tits, “Stability robustness analysis of uncertain discrete-time descriptor systems,” to appear in IFAC 2002.[18] L. El Ghaoui, R. Nikoukhah, and F. Delebecque, “LMITOOL: a package for LMI optimization,” Proc. 34nd CDC, New Orleans, Louisiana, vol. 3, pp. 3096-3101,1995[19] K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice-Hall, 1996.

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