具輸入及狀態延遲之模糊系統控制

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：42

、訪客IP：3.16.50.1

姓名

王毓淇(Yuchi Wang) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

具輸入及狀態延遲之模糊系統控制
(Stabilization of Fuzzy Retarded Systems with Input and State Delays)

相關論文

★ 強健性扇形區域穩定範圍之比較	★ 模糊系統混模強健控制
★ T-S模糊模型之建構、強健穩定分析與H2/H∞控制	★ 廣義H2模糊控制-連續系統線性分式轉換法
★ 廣義模糊控制-離散系統線性分式轉換法	★ H∞模糊控制－連續系統線性分式轉換法
★ H∞模糊控制—離散系統線性分式轉換法	★ 強健模糊動態輸出回饋控制-Circle 與 Popov 定理
★ 強健模糊觀測狀態回饋控制-Circle與Popov定理	★ H_infinity 取樣模糊系統的觀測型控制
★ H∞取樣模糊系統控制與觀測定理	★ H-ihfinity取樣模糊系統動態輸出回饋控制
★ H∞模糊系統控制-多凸面法	★ H∞模糊系統控制-寬鬆變數法
★ 時間延遲 T-S 模糊系統之強健 H2/H(Infinity) 控制與估測	★ 寬鬆耗散性模糊控制-波雅定理

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

本論文是研究延遲模糊系統(fuzzy systems) 所代表的系統穩定問題，
以及應用波雅定理於檢測條件上，來得到一較為寬鬆的檢測條件。
內容方面本論文將分為兩部分來進行討論，第一部份先推導一般性的延遲穩定條件，第二部分引入狀態擴充的延遲穩定條件，再引入多輸入延遲加以驗證波雅定理的應用。
本論文將在 LMI(Linear Matrix Inequality) 中探討一個時間延遲系統的穩定檢測條件。
藉由建立在Lyapunov-Krasovskii函數，將目前文獻中尚未完全處理的延遲參數，做一個完全性的整合。
並解決了傳統上延遲參數為時變的狀況，將微分後難以求解的積分項問題，重新整理以求得穩定解。
本論文同時也研究當輸入延遲增加的情況下，考慮系統的穩定情形，加入寬鬆環境下的條件並加以驗證波雅定理的實際應用。
本論文提供一套系統化的研究方法，研究延遲系統的穩定條件，並將在最後代入波雅定理探討求解的檢測條件，
進而達到Lyapunov-Krasovskii穩定的充要條件。

摘要(英)

In this study, a stabilization problem for continuous-time fuzzy systems
subject to multiple time-varying delays in both state and input variables is addressed.
The main objective is to design a stablilizing controller that stabilizes the aforementioned delay system.
Based on Lyapunov-Krasovskii functional and P’’olya theorem, sufficient stabilization conditions are stated in terms of
LMIs. Therefore, stabilizing controllers can be obtained easily with existing convex algorithms. Unlike existing methods,
polynomial theory is used to deal with input-delay term since this delay term introduces
an additional summation after defuzzification.
Lastly, three examples are given to illustrate
the advantages of the proposed machinery, yielding more relaxations when compared to existing methods.

關鍵字(中)

★ 萊布尼茲牛頓公式
★ T-S 模糊模型
★ 線性矩陣不等式
★ 波雅定理
★ Lyapunov-Krasovskii方程式

關鍵字(英)

★ Lyapunov-Krasovskii function
★ Leibniz-Newton formula
★ P'olya's theorem
★ LMI

論文目次

論文摘要 i
誌謝 iv
圖目 viii
第一章簡介 1
1.1 文獻回顧 1
1.2 研究動機 3
1.3 論文結構 4
1.4 符號標記 4
1.5 預備定理 5
第二章基礎理論概要介紹及系統架構 7
2.1 模糊邏輯控制器 7
2.1.1 模糊規則庫 7
2.2 系統架構 8
2.2.1 非線性模糊系統 8
2.2.2 狀態回饋控制器設計 9
第三章配方法 11
3.1 檢測延遲穩定條件 11
3.2 加入寬鬆條件 18
第四章狀態擴充矩陣與多輸入延遲之穩定條件 20
4.1 狀態矩陣擴充 20
4.1.1 檢測穩定條件 20
4.2 狀態擴充之寬鬆條件 28
第五章波雅定理 31
5.1 波雅定理(P'olya’sTheorem) 31
5.2 考慮多輸入延遲利用波雅定理 31
第六章離散時間延遲系統之架構 37
6.1 系統架構 37
6.1.1 離散時間延遲系統 37
6.1.2 狀態回饋控制器設計 38
6.2 離散時間使用配方法之穩定性 39
6.2.1 加入寬鬆條件 47
第七章電腦模擬 50
7.1 配方法 50
7.2 狀態擴充法 53
第八章結論與未來方向 66
8.1 總結 66
8.2 未來研究方向 67
參考文獻 68

參考文獻

[1] J. Wan and J. Lo, “LMI relaxations for nonlinear fuzzy control systems via homogeneous polynomials,” in The 2008 IEEE World Congress on Computational Intelligence, FUZZ 2008, Hong Kong, CN, June 2008, pp. 134–140.
[2] L. Li and X. Liu, “New results on delay-dependent robust stability criteria of uncertain fuzzy systems with state and input delays,” Information Sciences, vol.179, pp. 1134–1148, 2009.
[3] Y. Cao and P. Frank, “Robust H1 disturbance attenuation for a class of uncertain discrete-time fuzzy systems,” IEEE Trans. Fuzzy Systems, vol. 8, no. 4, pp. 406–415, Aug. 2000.
[4] R. Palhares, C. de Souza, and P. Peres, “Robust H1 filtering for uncertain discrete time state-delayed systems,” IEEE Trans. Signal Processing, vol. 49, no. 8, pp.1696–1703, Aug. 2001.
[5] C. de Souza, R. Palhares, and P. Peres, “Robust H1 filtering design for uncertain linear systems with multiple time-varying state delays,” IEEE Trans. Signal Processing, vol. 49, no. 3, pp. 569–576, Mar. 2001.
[6] Y. Lin and J. Lo, “H1 filter/control design for discrete-time Takagi-Sugeno fuzzy systems with time delays,” in Proc. 2004 Conf. Asia Contr., vol. 1, Melbourne,AU, Dec. 2004, pp. 1516–1522.
[7] ——, “Exponential stability of filtering problems for delay fuzzy systems,” in Proc.2004 IEEE Int’l Conf. Networking, Sensing and Control, vol. 2, Taipei, TW, Mar.2004, pp. 926–931.
[8] H. Wu and H. Li, “New approach to delay-dependent stability analysis and stabilization for continuous-time fuzzy systems with time-varying delay,” IEEE Trans.Fuzzy Systems, vol. 15, no. 3, pp. 482–493, June 2007.
[9] B. Chen, X. Liu, S. Tong, and C. Lin, “Guaranteed cost control of T-S fuzzy systems with state and input delays,” Fuzzy Set and Systems, vol. 158, pp. 2251–2267, 2007.
[10] ——, “New delay-dependent stabilization conditions of T-S fuzzy systems with constant delay,” Fuzzy Set and Systems, vol. 158, 2007.
[11] J. Kim, D. Oh, and H. Park, “Guaranteed cost and H1 filtering for time delay systems,” in Proc. the Amer. Contr. Conf., Arlington, VA, 2001, pp. 4014–4019.
[12] Y. Cao and P. Frank, “Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models,” Fuzzy Set and Systems, vol. 124,pp. 213–229, 2001.
[13] C. Lin, Q. Wang, and T. Lee, “Delay-dependent LMI conditions for stability and stabilization of T-S fuzzy systems with bounded time-delay,” Fuzzy Set and Systems, vol. 157, pp. 1229–1247, 2006.
[14] E. Tian and C. Peng, “Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay,” IEEE Trans. Fuzzy Systems, vol.157, pp. 544–559, 2006.
[15] M. Wu, Y. He, and J. She, “New delay-dependent stability criteria and stabilizing method for neutral systems,” IEEE Trans. Fuzzy Systems, vol. 49, no. 12, pp.2266–2271, Dec. 2004.
[16] Y. He, M. Wu, J. She, and G. Liu, “Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays,” Syst. & Contr. Lett., vol. 51, 2004.
[17] A. Sala and C. Ari˜no, “Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya’s theorem,”Fuzzy Set and Systems, vol. 158, pp. 2671–2686, 2007.
[18] V. Montagner, R. Oliveira, and P. Peres, “Necessary and sufficient LMI conditions to compute quadratically stabilizing state feedback controller for Takagi-sugeno systems,” in Proc. of the 2007 American Control Conference, July 2007, pp. 4059–4064.
[19] B. Chen, X. Liu, S. Tong, and C. Lin, “Robust fuzzy control of nonlinear systems with input delay,” Chaos, Solitons and Fractals, vol. 37, pp. 894–901, 2008.
[20] R. Oliveira and P. Peres, “Stability of polytopes of matrices via affine parameterdependent Lyapunov functions: Asymptotically exact LMI conditions,” Linear Algebra and its Applications, vol. 405, pp. 209–228, 2005.
[21] ——, “LMI conditions for the existence of polynomially parameter-dependent Lyapunov functions assuring robust stability,” in Proc. of 44th IEEE Conf. on Deci and Contr, Seville, Spain, Dec. 2005, pp. 1660–1665.
[22] ——, “LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions,” Syst. & Contr. Lett., vol. 55, pp. 52–61, 2006.
[23] ——, “Parameter-dependent LMIs in robust analysis: characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxatiions,” IEEE Trans. Automatic Control, vol. 52, no. 7, pp. 1334–1340, July 2007.
[24] A. Sala and C. Ari˜no, “Design of multiple-parameterization PDC controllers via relaxed condition for multi- dimensional fuzzy summations,”in Proc. of Fuzz-IEEE’07., London, UK, 2007, doi:10.1109/FUZZY.2007.4295495.
[25] X. Liu and Q. Zhang, “New approaches to H1 controller designs based on fuzzy observers for T-S fuzzy systems via LMI,” Automatica, vol. 39, pp. 1571–1582,2003.
[26] M. Teixeira, E. Assuncao, and R. Avellar, “On relaxed LMI-based design for fuzzy regulators and fuzzy observers,”IEEE Trans. Fuzzy Systems, vol. 11, no. 5, pp.613–623, 2003.
[27] K. Tanaka, T. Ikeda, and H.Wang,“Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs,” IEEE Trans. Fuzzy Systems, vol. 6,no. 2, pp. 250–265, May 1998.
[28] C.-H. Fang, Y.-S. Liu, S.-W. Kau, L. Hong, and C.-S. Lee,“A new LMI-based approach to relaxed quadratic stabilzation of T-s fuzzy control systems,"IEEE Trans. Fuzzy Systems, vol. 14, no. 3, pp. 386–397, 2006.

指導教授

羅吉昌

審核日期

2009-7-3

推文