本論文研究具結構參數擾動連續時間、線性、非時變系統的強健穩定控制器設計問題。相對於現有 合成方法易產生相當高階動態控制器的缺點，本文所提方法產生的控制器其階數與受控體同階或更低階，甚至可為零階(即靜態增益)，且控制器可具有指定的結構限制。本文應用互質分解理論與廣義KYP引理，推導出充分有解條件，其為線性矩陣不等式(linear matrix inequality, LMI)形式。本文特色之一為將合成或分析條件之中的全頻段區分為低頻段及高頻段，進行控制設計與效能分析，其可減少若干條件的保守性。本文提供數個例子驗證所提方法的確有效。

This paper is concerned with the problems of designing robust stabilizing controllers for continuous-time linear time-invariant systems subject to structured parametric uncertainty. Compared to the existing mu synthesis method which often produces high-order dynamic controllers, the method we proposed produces controllers whose order is no greater than that of the plant, including zero order (i.e, static gain case). Furthermore, the controllers can have specified structural limitations. Sufficient conditions for the existence of the controllers are derived in terms of linear matrix inequalities (LMIs) via application of the coprime factorization theory and the GKYP lemma. One feature of the proposed method is that the entire frequency range of the synthesis and/or analysis conditions are equivalently replaced by the union of a low and a high frequency ranges. This may reduce the conservativeness of the conditions. A few numerical examples are provided that demonstrates the effectiveness of the proposed methods.

中文摘要...........................................................................................................I
英文摘要.........................................................................................................II
目錄................................................................................................................III
圖目錄...........................................................................................................VI
表目錄.........................................................................................................IV
第一章 緒論		1
	1.1文獻回顧與研究動機	1
	1.2論文架構	2
第二章 背景知識	3
第三章 全階動態控制器設計	9
	3.1問題敘述	9
	3.2問題轉換	11
	3.3頻域條件之推導	16
	3.4時域條件之推導	20
	3.5模擬結果與討論	27
第四章 降階動態控制器設計	37
	4.1問題轉換	37
	4.2頻域條件之推導	37
	4.3時域條件之推導	37
	4.4模擬結果與討論	39
第五章 靜態輸出回授設計	47
	5.1問題轉換	47
	5.2頻域條件之推導	48
	5.3時域條件之推導	49
	5.4模擬結果與討論	53
第六章 結論與未來研究方向	62
參考文獻	63









圖目錄

圖2.1	 delta-P-K架構	4
圖2.2	 I-P-K架構	6
圖2.3	 Pdelta-Kdelta架構	6
圖3.1	 delta-P-K標準系統架構	9
圖3.2	等效轉移函數	11
圖3.3	 Phead-Khead系統架構	12
圖3.4	 Pdelta-Khead系統架構	13
圖3.5	 Pbar-Kbar系統架構	14










表目錄

表3.1	不同擾動時之閉回路極點Ⅰ	36
表4.1	不同擾動時之閉回路極點Ⅱ	46
表5.1	不同擾動時之閉回路極點Ⅲ	60
表5.2	強健穩定性能分析Ⅰ	61
表5.2	強健穩定性能分析Ⅱ	61

參考文獻

[1]	K. Zhou and J. C. Doyle, Essentials of Robust Control. Prentice Hall,1998.
[2]	P.M. Young, “Controller design with real parametric uncertainty,” Internat. J. Control, Vol. 65, pp. 469-509, 1996.
[3]	K. C. Goh, M.G. Safonov, and J.H., Ly, “Robust synthesis via bilinear matrix inequalities,” Int. J. Robust and Nonlinear Contr., vol. 6, no.9/10, pp. 1079-1095, 1996.
[4]	A.L. Tits and Y.S. Chou, “On mixed  synthesis,” Automatica, vol. 36, no . 7, 2000 , pp. 1077-1079.
[5]	G. Meinsma, Y. Shrivastava, and M. Fu, “Some properties of an upper Bound for ,” IEEE Trans. on Autom. Control, vol. 41, no. 9, pp. 1326-1330, 1996.
[6]	T. Iwasaki and S. Hara, “Generalized KYP lemma: Unified frequency domain inequalities with design applications,” IEEE Trans. Autom. Control, vol. 50, no. 1, pp. 41–59, Jan. 2005.
[7]	Y.S. Chou and Y.L. Chang, “Decentralised Output Feedback Synthesis With Restricted Finite Frequency Domain Specifications via generalized Kalman-Yakubovich-Popov lemma: A unified approach,” IET Control Theory and Applications, vol. 9, no. 10, pp .1615-1628, 2015.
[8]	A. Rantzer, “On the Kalman-Yakubovich-Popov lemma,” Syst. Control Lett., vol. 28, pp. 7–10, 1996.
[9]	Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: ‘Manual of LMI control toolbox’ (Math Works, Inc., 1995)