控制工程問題通常考慮設計一個控制器使系統兼具多個性能，這是控制領域廣為討論的議題，此即所謂多目標控制。C.W. Scherer 等人針對動態輸出回授(dynamic output feedback, DOF)控制器提出了一套非常傑出的多目標控制解法，其條件為線性矩陣不等式(linear matrix inequality, LMI)形式，可運用數值軟體有效求解。相較之下，靜態輸出回授(static output feedback, SOF)控制器容易實現，然而迄今尚未有類似的通用解法。
本論文延續近期一連續時線性非時變系統的新型靜態輸出回授合成方法，探討離散時間系統的 H-infinity 靜態輸出回授設計問題，並將此方法推廣至其他問題，如 H2性能控制、區域極點配置(regional pole placement)控制。末了，本論文將提出數值例子，模擬驗證所提方法之效能。

Control problems often consider the design of a controller such that the closed-loop system has certain desired properties. This has been a hot issue in the control field, which is called multi-objective control. An outstanding method for dynamic output feedback controller synthesis on this subject was provided by C. W. Scherer et al. The solvability conditions are in terms of linear matrix inequalities (LMIs), which can be efficiently solved by available software. In comparison, there lacks such a unified approach for static output feedback (SOF) synthesis, though the implementation of SOF is simpler.
    By following a new approach to SOF synthesis for continuous-time linear time-invariant systems, this thesis considers the problem of designing H-infinity SOF for discrete-time systems. Extension is made to the synthesis problems of other control performances, such as H2 control and regional pole placement. Finally, numerical example is given that establishes the effectiveness of the proposed method.

目錄
誌謝	i
中文摘要	ii
英文摘要	iv
圖目錄	vii
表目錄	viii
第一章	緒論	1
第二章	背景知識與問題敘述	3
2.1	H∞之離散時域性能	5
2.2	H2之離散時域性能	6
2.3	區域極點配置	7
2.4 PK合成架構	8
第三章	靜態控制器設計	11
3.1	H∞靜態控制器設計	13
3.1.1情況1	16
3.1.2情況2	18
3.1.3情況3	21
3.2	H2靜態控制器設計	23
3.2.1情況1	24
3.2.2情況2	26
3.2.3情況3	28
3.3	區域極點配置靜態控制器設計	30
3.3.1情況1	31
3.3.2情況2	32
3.3.3情況3	34
第四章	模擬結果	36
4.1 H∞控制	36
4.2 H2控制	39
4.3 區域極點配置控制	41
4.4多目標控制(H∞性能與區域極點配置)	43
第五章	結論	46
參考文獻	47


圖目錄
圖2. 1傳統架構	8
圖2. 2 PK架構	9
圖4. 1  之波德圖	37
圖4. 2閉迴路系統極點分布圖	38
圖4. 3閉迴路系統極點分布圖	40
圖4. 4區域極點配置控制器閉迴路系統極點分布圖	42
圖4. 5多目標控制 之波德圖	44
圖4. 6多目標控制閉迴路系統極點分布圖	45
 
 
表目錄
表2. 1符號標示	3
表4. 1 H∞控制結果	37
表4.2 H2控制結果	40
表4.3區域極點配置控制結果	42
表4. 4多目標控制器數據	44

[1] C. Scherer,P. Gahinet, and M. Chilali, Multiobjective output-feedback control via LMI optimization,” IEEE Trans. Autom. Control, vol. 42, 1997, pp. 896-911.
[2] V. L. Syrmos, C.T. Abdallah, P. Dorato, and K. Grigoriadis, “Static output feedback—A survey,” Automatica, vol. 33, no. 2, 1997, pp.125–137.
[3] V. Kucera and C.E. de Souza, “A necessary and sufficient conditionfor output feedback stabilizability,” Automatica, vol. 31, no. 9, 1995, pp.1357–1359.
[4] L.ElGhaoui,F. Oustry, and M.AitRami, “A cone complementarity linearization algorithm for static output-feedback and related problems,” IEEE Trans. Automat. Control, vol. 42, no. 8, 1997, pp.1171–1176.
[5] Y.Y. Cao, J. Lam, and Y.X. Sun, “Static output feedback stabilization: An LMI approach,” Automatica, vol. 34, no. 12, 1998, pp. 1641–1645.
[6] Y. He and Q. Wang, “An improved ILMI method for static output feedback control with application to multivariable PIDcontrol,” IEEE Transactions on Autom. Control, vol. 51, no. 10, 2006, pp.1678–1683.
[7] S.J. Kim and Y.H. Moon, “Structurally constrained H2 and H-infinity control: A rank-constrained LMI approach,” Automatica, vol. 42, no. 9, 2006, pp. 1583-1588.
[8] C.A.R. Crusius and A. Trofino, “Sufficient LMI conditions for outputfeedback control problems,” IEEE Trans. Autom. Control, vol. 44, no. 5, May 1999, pp. 1053–1057.
[9] D. Henrion and J.B. Lasserre, “Convergent relaxations of polynominal matrix inequalities and static output feedback,” IEEE Trans. Autom. Control, vol. 51, no. 2, 2006, pp. 192-202.
[10] G. Garcia, B. Pradin, and F. Zeng, “Stabilization of discrete time linear systems by static output feedback,” IEEE Trans. Autom. Control, vol.46, no. 12, 2001, pp. 1954–1958.
[11] J.C. Geromel, C.C. de Souza, and R.E. Skelton, “Static output feedback controllers: Stability and convexity,” IEEE Trans. Autom. Control, vol.43, no. 1, 1998, pp. 120–125.
[12] 周永山，科技部計畫報告。計畫報告名稱：H-infinity 靜態輸出回授之新型合成方法，執行期限：2017/08/01-2018/07/31。
[13] S. Boyd and C. Barratt, Linear Controller Design – Limits of Performance, Prentice-Hall, 1991
[14] M. C. de Oliveira, J. C. Geromel, J. Bernussou, “Extended H2 and H∞ characterizations and controller parametrizations for discrete-time systems,” International Journal on Control, vol. 75, no.9,2002, pp. 666–679.
[15] P. Gahinet, A. Nemirovski, A. J. Laub, M. Chilali, Manual of LMI Control Toolbox, Math Works, Inc, 1995.