本論文探討當線性非時變的離散系統模型具有凸多邊形不確定量時，如何利用線性矩陣不等式設計動態輸出回授控制器使得閉迴路系統滿足 DR 穩定，而且其轉移矩陣的 H2 範數和 H∞ 範數小於規範值 ru 的問題。論文中根據系統是否 DR 穩定分為兩部份。在論文前半部份，我們提出 H2 和 H∞ 的分析方法(現有文獻的結果僅為本論文的特例)，而且改善控制器的設計方法：在論文後半部份的內容，我們更近一步討論當系統需要滿足 DR 穩定時 H2 和 H∞ 的設計方法。本論文提出來的設計方法為線性矩陣不等式的充分條件，因此可以利用現有的軟體求解，在論文中舉數值模擬的例子來做說明。

The thesis considers the problems of designing a dynamic output feedback controller to discrete time systems with polytopic uncertainty so that the closed-loop systems are DR stable with their transfer matrices having H2 norm and H∞ norm bounded by a prescribed value ru. The formar part of the thesis provides less conservative LMI conditions for H2 and H∞ analysis and the output feedback control of discrete system than those appeared in the current research. While the latter part of the thesis extend the current research to DR stable with H2 and H∞ design. Finally, numerical examples are illustrated to show improvement of the propered result.

中文摘要 i
英文摘要 ii
目錄 iii
圖次 v
表次 vi
符號說明 vii
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 基本定義與結果 4
2-1 節　系統之 H2 和 H∞ 分析 4
2-2 節　基本性質 5
第三章 具凸多邊形不確定量之離散系統之強韌 H2 和 H∞ 分析 9
3-1 節 強韌 H2 分析 9
3-2 節 強韌 H∞ 分析 13
3-3 節 混合強韌 H2/H∞ 分析 16
3-4 節 數值模擬 17
第四章 具凸多邊形不確定量之離散系統之強韌 H2 和 H∞ 設計 21
4-1 節 問題描述 21
4-2 節 強韌 H2 設計 22
4-3 節 強韌 H∞ 設計 39
4-4 節 混合強韌 H2/H∞ 設計 42
4-5 節　數值模擬 48
第五章 具凸多邊形不確定量之離散系統的強健根叢集於 DR區域之強韌 H2 和 H∞ 設計 59
5-1 節　問題描述 59
5-2 節　根叢集於 DR區域之分析 60
5-3 節　根叢集於 DR區域之設計 62
5-4 節　根叢集於 DR區域之混合強韌 H2/H∞ 設計 65
5-5 節　數值模擬 68
第六章 結論 72
參考文獻

L. Xie, M. Fu, C.E.D. Souza, “ H∞ control and quadratic stabilization of systems with parameter uncertainty via output feedback,” IEEE Trans.Automat.Control, vol. 37, pp. 1253–1256, 1992.
T. Iwasaki. “Robust performance analysis for systems with norm-bounded time-varying structured uncertainty,” Proc. American Contr. Conf., 1994.
L. Yuan, L. E. K. Achenie, and W. Jiang, “Robust H∞ control for linear discrete-time systems with norm-bounded time varying uncertainty,” Syst. Control Lett., vol. 27, pp. 199–208, 1996.
P. Shi, E.K. Boukas, Y. Shi, and R.K. Agarwal, “Optimal guaranteed cost control of uncertain discrete time-delay systems,” J. Comput. Appl. Math., vol. 157, pp. 435–451, 2003.
M.C.D. Oliveira, J. Bernussou, J.C. Geromel, "A new discrete-time robust stability condition," System and Control letters, vol. 37, pp. 261–265, 1999.
J.C. Geromel, M.C.D. Oliveira, and J. Bernussou, “Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions,” Proc. 38th IEEE Conf. Decision Contr., 1999.
J. Daafouz, J. Bernussou, “Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties,” System and Control letters., vol. 43, pp. 355–359, 2001.
U. Shaked, “Improved LMI representations for analysis and design of continuous- time systems with polytopic type uncertainty,” IEEE Trans. Automat. Contr., vol. 46, pp. 652–656 , 2001.
Y. He, M. Wu, and J. H. She, “Improved bounded real lemma representation and H∞ control of systems with polytopic ncertainties,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 52, no. 7, pp. 380–383, Jul. 2005.
M.C.D. Oliveira, J.C. Geromel, and J. Bernussou, “Extended H2 and H∞ norm characterizations and controller parametrizations for discrete-time systems,” Int. J. Control, vol. 75, pp. 666–679, 2002.
C. Scherer, P. Ghainet, and M. Chilali, “Multiobjective output feedback control via LMI optimization,” IEEE Trans. Automat. Contr., vol. 42, pp. 896–911, July 1997.
M. Farhoodi, M. T. H. Beheshti, “Extended linear matrix inequality approach to multiobjective output-feedback controller design,” India Conference, pp. 542–547, 2008.
P. Gahinet, A. Nemirovski, A.Laub, and M. Chilali, The LMI Control Toolbox, Math Works Inc., 1995.
J.C. Geromel, J. Bernussou, and M.C.D. Oliveira, “H2-norm optimization with constrained dynamic output feedback controllers: Decentralized and reliable control,” IEEE Trans. Automat. Contr., vol. 44, pp. 1449–1454, 1999.
H. Miba, A. Kochbati, A. Zaafouri, and M. Ksouri, “An LMI approach to H2/H∞ synthesis for ploytopic uncertain systems,” IEEE International Conference on Systems, 2002.
L. Lu, R. Yang, and L. Xie, “Robust H2 and H∞ control of discrete-time systems with polytopic uncertainties via dynamic output feedback,” In American Control Conference, pp. 4315–4320, Portland, OR, June 2005.
J. Bernussou, J.C. Geromel, and R.H. Korogui, “On robust output feedback control for polytopic systems,” 44th IEEE CDC-ECC ’05, pp. 5018–5023, 2005.
J.C. Geromel, R.H. Korogui, and J. Bernussou, “H2 and H∞ Robust output feedback control for continuous-time polytopic systems,” IET Control Theory and Applications, pp. 1541–1549, 2007.
C.P. Wei, “Robust H2 and H∞ output feedback control via parameter - dependent Lyapunov functions,” lab meeting report, 2009.
R. Huajun, “Non-fragile H∞ control based on dynamic output feedback for a class of linear discrete-time systems with time-varying delay,” Control Conference, 2010.
D.L. Wen, and G.H., Yang, “Dynamic output feedback H∞ control for networked control systems with random consecutive packet dropouts,” Control and Decision Conference, 2010.
S. Shi , Q. Zhang, and Z. Yuan, “Exponential stability and L2 gain analysis for a class of faulty systems,” International Journal of Systems Science, vol. 42, no. 3, pp. 377–387, 2011.
G.S. Deaecto, and J.C. Geromel, “H∞ control for continuous-time switched linear systems,” Journal of Dynamic Systems, Measurement, and Control, vol. 132, 2010.
D. Peaucelle, D. Arzelier, O. Bachelier, and J. Bernussou, “A new robust D-stability condition for real convex polytopic uncertainty,” Syst. Control Lett., vol. 40, no. 1, pp. 21–30 , 2000.
M. Chilali, P. Gahinet, “H∞ design with pole placement constraints: an LMI approach,” IEEE Trans. Automat. Control, AC-41 (3), pp. 358–367, 1996.
D. Arzelier, D. Henrion, D. Peaucelle, “Robust D-stabilization of a polytope of matrices,” Int. J. Control, vol. 75, pp. 744–752, 2002.
E.N. Gonçalves, W.E.G. Bachur, R.M. Palhares and R.H.C. Takahashi, “Robust H2/H∞ reference model dynamic output-feedback control synthesis,” Int. J. Control, vol. 84, no. 12, pp. 2067–2080, 2011.
S. Boyd, L.E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
L.E. Ghaoui, F. Oustry and M. AitRami, “A cone complementarity linearization algorithm for static output-feedback and related problems,” IEEE Trans. Automat. Contr., vol. 42, pp. 1171–1176, 1997.
F. Leibfritz, “An LMI-based algorithm for designing suboptimal static H2/H∞ output feedback controllers,” SIAM J. Control Optim., vol. 39, pp.1711–1735, 2001.