臺灣博碩士論文加值系統

本論文對間時廣義系統提出一以嚴格線性矩陣不等式為條件的界實引理。與已有的非嚴格線性矩陣不等式的條件相比，此一新的條件較便利於數值計算及方便使用Matlab的LMI Control Toolbox來作模擬設計。根據此一結果，文中進一步探討以狀態迴授設計 H-infinite 控制的問題。吾人推得一以嚴格線性矩陣不等式為充份條件的結果，根據它的解以便建構出符合閉迴路系統設計準則的迴授增益矩陣。更進一步地，我們探討了不確定間時廣義系統的強韌 H-infinite 控制及根叢集在所指定圓內的問題。我們分別針對具有非時變範數有界的不確定量及凸多邊形不確定量的兩類不確定系統，亦推得一些以嚴格線性矩陣不等式為充份條件的分析及設計結果。文末並舉例說明之。

This thesis presents strict LMI conditions for the bounded real lemma of discrete descriptor systems. Compared with existing nonstrict LMI conditions, the proposed new conditions are more tractable and reliable in numerical computations, in the sense that they can be tested easily by using the LMI Control Toolbox of Matlab. Based on the strict LMI conditions, the state feedback design for H-infinite control problem is also addressed. A sufficient LMI condition is derived so that the constructed feedback gain matrix from its solution will meet the design criteria of the closed-loop systems. Furthermore, we can probe into the problems of robust H-infinite control and pole-clustering in a disk for uncertain discrete descriptor systems subject to time-invariant norm-bounded uncertainty and convex polytopic uncertainty in the state matrix, respectively. Some sufficient LMI conditions are derived for analysis and design of these problems as well. Numerical examples are included to illustrate the results.

摘要 i
符號表 v
第一章 緒論 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 間時廣義系統之界實引理及根叢集在圓內之分析 4
2-1節 間時廣義系統之基本性質 4
2-2節 間時廣義系統之界實引理 7
2-3節 間時廣義系統根叢集在圓內之限制 8
第三章 不確定間時廣義系統根叢集在圓內之強韌 H-infinite 分析 9
3-1節 以嚴格線性矩陣不等式為條件之界實引理 9
3-2節 根叢集在圓內及 H-infinite 限制之分析 17
3-3節 範數有界的不確定系統 21
3-3-1節 強韌 H-infinite 分析 22
3-3-2節 根叢集在圓內之強韌 H-infinite 分析 23
3-4節 凸多邊形不確定系統 25
3-4-1節 強韌 H-infinite 分析 26
3-4-2節 根叢集在圓內之強韌 H-infinite 分析 30
第四章 狀態迴授控制器設計 33
4-1節 間時廣義系統之 H-infinite 設計 33
4-2節 範數有界的不確定系統 37
4-2-1節 強韌 H-infinite 設計 37
4-2-2節 根叢集在圓內之強韌 H-infinite 設計 39
4-3節 凸多邊形不確定系統 41
4-3-1節 強韌 H-infinite 設計 41
4-3-2節 根叢集在圓內之強韌 H-infinite 設計 43
第五章 數值模擬 44
第六章 結論 56
參考文獻 57
索引 60

[1] G. C. Verghese, B. C. Levy, and T. Kailath, “A generalized state-space for singular systems”, IEEE Trans. Automat. Control, vol. 26, pp. 811-831, 1981.[2] J. D. Cobb, “Feedback and pole-placement in descriptor variable systems”, Int. J. Control, vol. 33, pp. 1135-1146, 1981.[3] J. D. Cobb, “Controllability, observability, and duality in singular systems”, IEEE Trans. Automat. Control, vol. 29, pp. 1076-1082, 1984.[4] F. L. Lewis, “Preliminary notes on optimal control for singular systems”, Proc. IEEE Conference on Decision and Control, pp. 266-272, 1985.[5] D. J. Bender and A. J. Laub, “The linear-quadratic optimal regulator for descriptor systems”, IEEE Trans. Automat. Control, vol. 32, pp. 672-687, 1987.[6] D. J. Bender and A. J. Laub, “The linear-quadratic optimal regulator for descriptor systems:discrete-time case”, Automatica, vol. 23, pp. 71-85, 1987.[7] Z. Zhou, M. A. Shayman, and T. J. Tarn, “Singular systems:a new approach in the time domain”, IEEE Trans. Automat. Control, vol. 32, pp. 42-50, 1987.[8] L. Dai, Singular Control, System-Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1989.[9] K. Furuta and S. Phoojaruenchanachai, “An algebraic approach to discrete-time H-infinite control problems”, Proc. of ACC, San Diego, CA, pp. 3067-3072, 1990.[10] H. S. Wang, C. F. Yung, and F. R. Chang, “Bounded real lemma and H-infinite control for descriptor systems”, IEE Proc. Control Theory Appl., vol. 145, no. 3, pp. 316-322, 1998.[11] M. Sampei, T. Mita, Y. Chida, and M. Nakamichi, “A direct approach to H-infinite control problems using bounded real lemma”, Proc. of the 28th IEEE CDC, pp. 1494-1499, 1989.[12] S. Xu and C. Yang, “H-infinite state feedback control for discrete singular systems”, IEEE Transactions on Automatic Control, vol. 45, no. 7, pp. 1405-1409, 2000.[13] P. Gahinet, A. Nemirovski, A. Laub, and M. Chilali, The LMI Control Toolbox Math Works Inc., 1995.[14] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, SIAM, Philadelphia, 1994.[15] S. Xu and C. Yang, “Stabilization of discrete-time singular systems:a matrix inequalities approach”, Automatica, pp. 1613-1617, 1999.[16] I. Masubuchi, Y. Kamitane, A. Ohara, and N. Suda, “H-infinite control for descriptor systems:a matrix inequalities approach”, Automatica, vol. 33, no. 4, pp. 669-673, 1997.[17] 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.[18] C. H. Fang and L. Lee, “Stability robustness analysis of uncertain discrete-time descriptor systems”, accepted by IFAC Congress, 2002.[19] E. Uezato and M. Ikeda, “Strict LMI conditions for stability, robust stabilization, and H-infinite control of descriptor systems”, Proc. IEEE Conference on Decision and Control, pp. 4092-4097, 1999.[20] M. Chilalij, P. Gahinet, and P. Apkarian, “Robust pole placement in LMI regions”, IEEE Trans. Automat. Control, vol. 44, pp. 2257-2270, 1999.[21] M. Chilali and P. Gahinet, “H-infinite design with pole placement constraints:an LMI approach”, IEEE Trans. Automat. Control, vol. 41, pp. 358-367, 1996.[22] K. L. Hsiung and L. Lee, “Pole-clustering characterization via LMI for descriptor systems”, Proc. of the 36th IEEE CDC, pp. 1313-1314, 1997.[23] 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, vol. G, pp. 209-214, 1996.[24] S. Xu, C. Yang, Y. Niu, and J. Lam, “Robust stabilization for uncertain discrete singular systems”, Automatica, vol. 37, pp. 769-774, 2001.[25] J. L. Chen and L. Lee, “Robust pole clustering for descriptor systems with norm-bounded uncertainty”, Proc. of 2001 ACC, pp. 2953-2954, 2001.[26] S. Xu, J. Lam, and C. Yang, “Robust H-infinite control for uncertain discrete singular systems with pole placement in a disk”, Systems & Control Letters, vol. 43, pp. 85-93, 2001.[27] J. C. Huang, H. S. Wang, and F. R. Chang, “Robust H-infinite control for uncertain linear time-invariant descriptor systems”, IEE Proc.-Control Theory Appl., vol. 147, no. 6, pp. 648-654, 2000.[28] K. M. Zhou and J. C. Doyle, Essentials of Robust Control, Prentice-Hall Inc., New Jersey, 1998.[29] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1985.[30] M. C. de Oliveira, J. Bernussou, and J. C. Geromel, “A new discrete-time robust stability condition”, Systems & Control Letters, vol. 37, pp. 261-265, 1999.