本篇論文利用線性矩陣不等式來設計靜態輸出迴授控制器，使得閉迴路系統的極點均落於預先選定的線性矩陣不等式區域Ｄ內，針對所推得充分條件的必要性也進一步分析探討，並將結果推廣到廣義的線性矩陣不等式區域ＤＲ。除了極點放置外，本論文更結合在強韌控制中常見的系統性能要求：Ｈ2 與 Ｈinf 設計，而達成多目標控制設計。為了考慮所設計之靜態輸出迴授控制器的強韌性，我們探討了範數有界、正實、以及凸多邊形三類不確定量，分別推導出以線性矩陣不等式表示之二次Ｄ穩定的設計條件，並討論了Ｄ區域下的界實性與正實性及其廣義性。在各個章節的最後都有數值範例說明所推得的結果。

In this thesis, LMI approach is employed to design a static output feedback controller so that all poles of the considered closed-loop continuous-time system are located within a prescribed LMI region, named D region. Based on the coordinate transformation, an analysis about the derived LMI-based sufficient condition is also established. The result is, moreover, extended to treat pole placement in the generalized LMI region, denoted by DR region. In addition to the requirement on pole location, two commonly exploited system performances in robust control, i.e. the H2 and Hinf designs, are also considered so that the multiobjective control by static output feedback is investigated in this thesis. To address robustness issue of the designed controllers, three different uncertainty descriptions, i.e. norm bounded uncertainty, positive real uncertainty, and polytopic uncertainty, are considered and LMI conditions for quadratic D stabilization by static output feedback have been derived. The bounded realness and positive realness with respect to an LMI D region are studied as well. Numerical examples are provided in the end of chapters 3, 4, and 5 to illustrate the obtained results there.

摘要 i
符號表 iv
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 基本性質 4
第三章 靜態輸出迴授之極點放置問題 7
3-1 節 WD-問題 7
3-2 節 充分性之分析 9
3-3 節 廣義線性矩陣不等式區域 12
3-4 節 數值模擬 16
第四章 靜態輸出迴授之多目標設計 19
4-1 節 H2性能 19
4-2 節 混合H2/Hinf性能 21
4-3 節 數值模擬 24
第五章 靜態輸出迴授之極點放置強韌性問題 26
5-1 節 範數有界不確定量 26
5-2 節 正實不確定量 29
5-3 節 凸多邊形不確定量 38
5-4 節 數值模擬 40
第六章 結論 44
參考文獻 45
索引 47

[1] V. Blondel, M. Gevers, and A. Lindquist, “Survey on the state of systems and control,” European Journal of Control, vol. 1, pp. 5-23, 1995.
[2] P. L. D. Peres, J. C. Geromel, and S. R. Souza, “Optimal control by output feedback,” Proc. of the 32nd IEEE Conf. on Decision and control , San Antonio, TX, pp. 102-107, 1993.
[3] Y. Y. Cao, J. Lam, and Y. X. Sun, “Static output feedback stabilization: an ILMI approach,” Automatica, vol.34, no.12, pp. 1641-1645, 1998.
[4] D. Peaucelle, D, Arzelier, and R. Bertrand, “Ellipsoidal sets for static output feedback,” Proc. of the 15th IFAC World Congress, Barcelona, July 2002.
[5] V. L. Syrmos, C. T. Abdallah, P. Dorato, and K. Grigoriadis, “Static output feedback－a survey,” Automatica, vol.33, no.3, pp. 125-137, 1996.
[6] M. Chilali and P. Gahinet, “ design with pole placement constraint: an LMI approach,” IEEE Trans. on Automatic Control, vol. 41, no.3, pp. 358-367, 1996.
[7] M. Chilali, P. Gahinet, and P. Apkarian, “Robust pole placement in LMI regions,” IEEE Trans. on Automatic Control, vol. 44, no.12, pp. 2257-2269, 1999.
[8] D. Peaucelle, D. Arzelier, O. Bachelier, and J. Bernusson, “A new -stability condition for real convex polytopic uncertainty,” Systems and Control Letters, vol. 40, pp. 21-30, 2000.
[9] H. Kimura, “Pole assignment by gain output feedback,” IEEE Trans. On Automatic Control, vol. 20, no.4, pp. 509-516, 1975.
[10] E. Davison and S. Wang, “On pole assignment in linear multivariable systems using output feedback,” IEEE Trans. On Automatic Control, vol. 20, no.4, pp. 516-518, 1975.
[11] V. L. Syrmos and F. L. Lewis, “A bilinear formulation for the output feedback problem in linear systems,” IEEE Trans. On Automatic Control, vol. 39, no.2, pp. 410-414, 1994.
[12] E. B. Castelan, J. C. Hennet, and E. R. L. Villarrel, “Quadratic characterization and use of output stabilizable subspace,” IEEE Trans. on Automatic Control, vol. 48, no.4, pp. 654-660, 2003.
[13] P. Lancaster and M. Tismenetsky, The Theory of Matrices, 2nd ed., Academic Press Inc., 1985.
[14] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Studies in Applied Mathematic, Philadelphia, 1994.
[15] C. A. R. Crusius and A. Trofino, “Sufficient LMI condition for output feedback control problems,” IEEE Trans. On Automatic Control, vol. 44, no.5, pp. 1053-1057, 1999.
[16] C. H. Kuo, Robust Pole-Clustering in Generalized LMI Regions Analysis for Descriptor Systems, Master thesis, NSYSU, Taiwan, ROC, 2002.
[17] W. M. Haddad and D. S. Bernstein, “Robust stabilization with positive real uncertainty: beyond the small gain theorem,” Systems & Control letters, vol. 17, pp. 191-208, 1991.
[18] C. H. Kuo and C. H. Fang, “Stabilization of uncertain linear systems via static output feedback control,” Proc. of R.O.C. Automatic Control Conference, pp. 1607-1611, 2003.
[19] A. Trofino, A. S. Bazanella, and A. Fischman, “Designing robust controllers with operating point tracking,” Proc. of IFAC Conf. Systems Structure and Control, Nantes, France, June 1998.