Title page for 953203073


[Back to Results | New Search]

Student Number 953203073
Author Sheng-Yi Gau(高聖鎰)
Author's Email Address angra444@yahoo.com.tw
Statistics This thesis had been viewed 1287 times. Download 397 times.
Department Mechanical Engineering
Year 2007
Semester 2
Degree Master
Type of Document Master's Thesis
Language zh-TW.Big5 Chinese
Title dissipative control for singularly perturbed fuzzy systems with Polya theorem
Date of Defense 2008-06-20
Page Count 89
Keyword
  • dissipative control
  • Polya theorem
  • singularly perturbed systems
  • Abstract In this thesis, we propose a general quadratic dissipative state feedback control method to solve a stabilization problem for fuzzy singularlyperturbed system. The problem covers the bounded real, positive realand sector-bounded performance as a special case by choosing the corresponding
    quadratic supply rate. Moreover, we also prove necessary
    and sufficient conditions to state feedback controllers ensuring quadratic stability for Takagi-Sugeno fuzzy systems in theory. But our main objective is to generate a family of linear matrix inequalities based on an extension of P´olya’s theorem(a.k.a Matrix-valued P´olya’s heorem).
    The proposed conditions are stated as progressively less conservative sets of linear matrix inequalities, allowing us to obtain a solution for the quadratic stabilizability problem whenever a solution exists.
    Table of Content 論文摘要I
    Abstact III
    誌謝IV
    圖目IX
    第一章簡介1
    1.1 文獻回顧¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 1
    1.2 研究動機¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 2
    1.3 論文結構¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 3
    1.4 符號標記¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 4
    1.5 預備定理¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 5
    第一部份: 耗散性控制(Dissipative Control) 6
    第二章系統架構與穩定條件6
    2.1 廣義非線性系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 6
    2.2 定義一(耗散系統) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 7
    2.3 奇異攝動耗散模糊系統的之分析與綜合¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 8
    2.3.1 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 8
    2.3.2 備註¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 10
    2.3.3 定理一(連續時間系統) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 11
    2.3.4 定理二(離散時間系統) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 14
    第三章狀態回饋控制器設計18
    3.1 狀態回饋控制器數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 18
    3.2 奇異攝動耗散模糊控制系統之分析與綜合¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 19
    3.2.1 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 19
    3.2.2 定理三(連續時間系統) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 21
    3.2.3 定理四(離散時間系統) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 22
    3.2.4 備註¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 24
    第四章電腦模擬26
    4.1 連續控制系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 26
    4.1.1 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 26
    4.1.2 求解¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 29
    4.1.3 備註(求解結果之討論) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 39
    4.2 離散控制系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 40
    4.2.1 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 40
    4.2.2 求解¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 42
    4.2.3 備註(求解結果之討論) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 51
    第二部份: 波雅定理53
    第五章控制系統架構與波雅定理53
    5.1 定理五(波雅定理)[54] ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 53
    5.1.1 備註¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 53
    5.2 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 54
    5.3 狀態回饋控制器數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 55
    5.4 定義二(二次穩定) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 57
    5.5 定理六¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 58
    5.5.1 備註¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 59
    第六章狀態回饋控制器設計61
    6.1 連續系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 61
    6.1.1 定理七(連續系統穩定充要條件) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 62
    6.2 離散系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 63
    6.2.1 定理八(離散系統穩定充要條件) ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 64
    6.3 範例¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 65
    6.3.1 備註¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 67
    第七章電腦模擬68
    7.1 連續控制系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 68
    7.1.1 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 68
    7.2 離散控制系統¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 74
    7.2.1 數學模型¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 74
    第八章結論與未來方向80
    8.1 總結¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 80
    8.2 未來研究方向¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 81
    參考文獻82
    Reference [1] S. Xie, L. Xie, and C. de Souza, “Robust dissipative control for linear systems
    with dissipative uncertainty,” Int. J. Contr., vol. 70, no. 2, pp. 169–191, 1998.
    [2] J. Willems, “Dissipative dynamical systems-Part 1: General theory,” Arch. Rational
    Mech. Analy., vol. 45, pp. 321–351, 1972.
    [3] ——, “Dissipative dynamical systems-Part 2: Linear systems with quadratic supply
    rates,” Arch. Rational Mech. Analy., vol. 45, pp. 352–393, 1972.
    [4] D. Hill and P. Moylan, “The stability of nonlinear dissipative systems,” IEEE
    Trans. Automatic Control, vol. 21, pp. 708–711, 1976.
    [5] ——, “Dissipative dynamical systems: Basic input-output and state properties,”
    J. franklin Inst., vol. 309, pp. 327–357, 1980.
    [6] L. Xie, “Robust output feedback dissipative control for uncertain nonlinear systems,”
    in Intelligent Control and Automation, 2004. WCICA 2004. Fifth World
    Congress on, vol. 1, Hangzhou, China, June 2004, pp. 809–813.
    [7] S. Yuliar and M. James, “General dissipative output feedback control for nonlinear
    systems,” in Decision and Control, 1995., Proceedings of the 34th IEEE
    Conference on, vol. 3, New Orleans, LA, Dec. 1995, pp. 2221–2226.
    [8] S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities
    in System and Control Theory. SIAM.
    [9] P. Gahinet, A. Nemirovskii, A. Laub, and M. Chilali, “The LMI control toolbox,”
    in Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on, Lake
    Buena Vista, FL, USA, Dec. 1994, pp. 2038–2041.
    [10] Y. Nesterov and A. Nemirovskii, Interior Point Polynomial Methods in Convex
    Programming: Theory and Algorithms. Philadelphia, PA: SIAM, 1994.
    [11] S. Yuliar and M. James, “Stabilization of linear systems with sector bounded
    nonlinearities at the input and output,” in Proc. of the 36th Conf. on Deci. &
    Contr., vol. 3, Kobe, JP, Dec. 1996, pp. 4759–4764.
    [12] S. Gupta, “ Robust Stabilization of Uncertain Systems Based on Energy Dissipation
    Concepts,” NASA Contractor Report 4713, 1996.
    [13] V. Chellaboina, W. Haddad, and A. Kamath, “A dissipative dynamical systems
    approach to stability analysis of time delay systems,” in American Control Conference,
    2003. Proceedings of the 2003, vol. 1, Denver,Colorado, June 2003, pp.
    363–368.
    [14] L. Xie, “Robust Dissipative Control for Uncertain Descriptor Linear Systems with
    Time Delay,” in Intelligent Control and Automation, 2006. WCICA 2006. The
    Sixth World Congress on, vol. 1, Dalian, China, June 2006, pp. 2327–2333.
    [15] Z. Tan, Y. Soh, and L.Xie, “Dissipative control for linear discrete-time systems,”
    Automatica, vol. 35, pp. 1557–1564, 1999.
    [16] S. Yuliar, M. James, and J. Helton, “Dissipative Control Systems Synthesis with
    Full State Feedback,” Mathematics of Control, Signals, and Systems, 1998.
    [17] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications
    to modelling and control,” IEEE Trans. Syst., Man, Cybern., vol. 15, no. 1, pp.
    116–132, Jan. 1985.
    [18] K. Tanaka and H. Wang, Fuzzy Control Systems Design: A Linear Matrix Inequality
    Approach. New York, NY: John Wiley & Sons, Inc., 2001.
    [19] H. Uang, “On the dissipativity of nonlinear systems: fuzzy control approach,”
    Fuzzy Set and Systems, vol. 156, pp. 185–207, 2005.
    [20] J. Lo and J. Wan, “Dissipative control to fuzzy systems with nonlinearity at
    the input,” in The 2007 CACS International Automatic Control Conference,
    Taichung,Tw, Nov. 2007, pp. 329–334.
    [21] J. Lo and D. Wu, “Dissipative filtering for nonlinear fuzzy systems,” in The 2007
    CACS International Automatic Control Conference, Taichung,Tw, Nov. 2007, pp.
    623–627.
    [22] Y. Li, Y. fu, and G. Duan, “Robust dissipative control for T-S fuzzy systems with
    time-delays,” in IEEE ISIE, Montreal, Ca, July 2006, pp. 97–101.
    [23] L. CAO and S. H. M., “Output feedback stabilization of linear systems with a
    singular perturbation model,” 2002, pp. 1627–1632.
    [24] J. Dong and G.-H. Yang, “H1 control for fast sampling discrete-time singularly
    perturbed systems,” Automatica, vol. 44, pp. 1385–1393, Feb. 2008.
    [25] Z. Ning-fan, S. Min-hui, and ZOU-Yun., “H1 control for singularly perturbed
    system: a method based on sigular system cotroller design,” in IET Control Theory
    Appl., vol. 24, no. 5, 2007, pp. 701–706.
    [26] S. Pang, H.-W. Wang, and G.-M. Lu., “Robust Control of Singularly Perturbed
    Systems and Simulations,” in IET Control Theory Appl., vol. 24, no. 4, 2005, pp.
    19–22.
    [27] H. Liu, F. Sun, and Z. Sun, “Stability analysis and synthesis of fuzzy singularly
    perturbed systems,” IEEE Trans. Fuzzy Systems, vol. 13, no. 2, pp. 273–284, Apr.
    2005.
    [28] E. Fridman, “State feedback H1 control of nonlinear singularly perturbed systems,”
    Int’l J. of Robust and Nonlinear Control, vol. 11, pp. 1115–1125, 2001.
    [29] H. Liu, F. Sun, and Y. Hu, “H1 control for fuzzy singularly perturbed systems,”
    Fuzzy Set and Systems, vol. 155, pp. 272–291, 2005.
    [30] W. Assawinchaichote and S. Nguang, “H1 fuzzy control design for nonlinear singularly
    perturbed systems with pole placement constraints: an LMI approach,”
    IEEE Trans. Syst., Man, Cybern. B: Cybernetics, vol. 34, no. 1, pp. 579–588, Feb.
    2004.
    [31] ——, “H1 filtering for fuzzy singularly perturbed systems with pole placement
    constraints: an LMI approach,” IEEE Trans. Signal Processing, vol. 52, no. 6, pp.
    1659–1667, June 2004.
    [32] G. Feng, “A survey on analysis and design of model-based fuzzy control systems.”
    IEEE Trans. Fuzzy Systems, vol. 14, no. 5, pp. 676–697, Oct. 2006.
    [33] A. Sala, T. Guerra, and R. Babuska, “Perspectives of fuzzy systems and control,”
    Fuzzy Set and Systems, vol. 156, pp. 432–444, June 2005.
    [34] 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.
    [35] T. Guerra and L. Vermeiren, “LMI-based relaxed nonquadratic stabilization conditions
    for nonlinear systems in the Takagi-Sugeno’s form,” Automatica, vol. 40,
    pp. 823–829, 2004.
    [36] S. Zhou, G. Feng, J. Lam, and S. Xu, “Robust H1 control for discrete-time fuzzy
    systems via basis-dependent Lyapunov functions,” Information Sciences, vol. 174,
    pp. 197–217, 2004.
    [37] S. Zhou, J. Lam, and W. Zheng, “Control Design for Fuzzy Systems Based on
    Relaxed Nonquadratic Stability and H1 Performance Conditions,” IEEE Trans.
    Fuzzy Systems, vol. 15, pp. 188–199, 2007.
    [38] K. Tanaka, T. Hori, and H. Wang, “A multiple Lyapunov Function Approach
    to Stabilization of Fuzzy Control Systems,” IEEE Trans. Fuzzy Systems, vol. 11,
    no. 4, pp. 582–589, Aug. 2003.
    [39] K. Tanaka, H. Ohtake, and H. Wang, “A Descriptor System Approach to Fuzzy
    Control System Design via Fuzzy Lyapunov Functions,” IEEE Trans. Fuzzy Systems,
    vol. 15, pp. 333–341, June 2007.
    [40] M. de Oliveira, J. Geromel, and J. Bernussou, “Extended H2 and H1 norm characterizations
    and controller parameterizations for discrete-time systems,” Int. J.
    Contr., vol. 75, no. 9, pp. 666–679, 2002.
    [41] E. Kim and H. Lee, “New approaches to relaxed quadratic stability condition of
    fuzzy control systems,” IEEE Trans. Fuzzy Systems, vol. 8, no. 5, pp. 523–534,
    Oct. 2000.
    [42] 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
    [43] 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.
    [44] 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.
    [45] S.-W. Kau, H.-J. Lee, C.-M. Yang, C.-H. Lee, L. Honga, and C.-H. Fang, “Robust
    H1 fuzzy static output feedback control of T-S fuzzy systems with parametric
    uncertainties,” Fuzzy Set and Systems, vol. 158, pp. 135–146, 2007.
    [46] B. Ding, H. Sun, and P. Yang, “Further studies on LMI-based relaxed stabilization
    conditions for nonlinear systems in Takagi-Sugeno’s form,” Automatica, vol. 43,
    pp. 503–508, 2006.
    [47] D. Ramos and P. Peres, “An LMI condition for the robust stability of uncertain
    continuous-time linear systems,” IEEE Trans. Automatic Control, vol. 47, no. 4,
    pp. 675–678, Apr. 2002.
    [48] M. de Oliveira and J. Geromel, “A class of robust stability conditions where linear
    parameter dependence of the Lyapunov function is a necessary condition for arbitrary
    parameter dependencestar,” Syst. & Contr. Lett., vol. 54, pp. 1131–1134,
    Nov. 2005.
    [49] R. Oliveira and P. Peres, “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.
    [50] R. C. Oliveira and P. L. Peres, “LMI conditions for robust stability analysis based
    on polynomially parameter-dependent Lyapunov functions,” Syst. & Contr. Lett.,
    vol. 55, pp. 52–61, Jan. 2006.
    [51] M. de Oliveira, J. Bernussou, and J. Geromel, “A new discrete-time robust stability
    condition,” Syst. & Contr. Lett., vol. 37, pp. 261–265, 1999.
    [52] J. Daafouz and J. Bernussou, “Parameter dependent Lyapunov functions for discrete
    time systems with time varying parametric uncertainties,” Syst. & Contr.
    Lett., vol. 43, pp. 355–359, Aug. 2001.
    [53] C. Arino and A. Sala, “Design of multiple-parameterisation PDC controllers via
    relaxed conditions for multi-dimensional fuzzy summations,” in Fuzzy Systems
    Conference, 2007. FUZZ-IEEE 2007. IEEE International, 2007, pp. 1–6.
    [54] G. Hardy, J. Littlewood, and G. P´olya, Inequalities, second edition. Cambridge,
    UK.: Cambridge University Press, 1952.
    [55] V. Power and B. Reznick, “A new bound for P´olya’s Theorem with applications to
    polynominals positive on polyhedra,” J. Pure Appl. Algebra, vol. 164, pp. 221–229,
    2001.
    [56] J. de Loera and F. Santos, “An effective version of Polya’s theorem on positive
    definite forms,” Journal of Pure and Applied Algebra, vol. 108, pp. 231–240, 1996.
    [57] C. Scherer, “Higher-order relaxations for robust LMI problems with verifications
    for exactness,” in Decision and Control, 2003. Proceedings, Maui,Hawaii, USA,
    Dec. 2003, pp. 4652–4657.
    [58] ——, “Relaxations for robust linear matrix inequality problems with verifications
    for exactness,” SIAM Journal on Matrix Analysis and Applications, vol. 27, pp.
    365–395, 2005.
    [59] 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, 2007, doi:10.1016/j,fss.2007.06.016.
    [60] 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.
    [61] V. Montagner, R. Oliveira, P. Peres, and P.-A. Bliman, “Linear matrix inequality
    characterisation for H1 and H2 guaranteed cost gain-scheduling quadratic stabilisation
    of linear time-varying polytopic systems,” Control Theory and Applications,
    IET, vol. 1, pp. 1726–1735, 2007.
    [62] R. Oliveira and P. Peres, “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
    [63] V. F. Montagner, R. C. L. F. Oliveira, and P. L. D. Peres, “ Necessary and sufficient
    LMI conditions to compute quadratically stabilizing state feedback controllers for
    Takagi-Sugeno systems,” in American Control Conference, 2007. ACC ’07, New
    York City, USA, 2007, pp. 4059–4064.
    [64] W. Assawinchaichote, S. Nguang, and P. Shi, “H1 output feedback control design
    for uncertain fuzzy singularly perturbed systems: an LMI approach,” Automatica,
    vol. 40, pp. 2147– 2152, Sept. 2004.
    [65] C. Scherer, “Relaxations for robust linear matrix inequality problems with verification
    for exactness,” SIAM J. Matrix Anal.Appl., vol. 27, no. 2, pp. 365–395,
    2005.
    [66] C. Scherer, P. Gahinet, and M. Chilali, “Multiobjective output-feedback control
    via LMI optimization,” IEEE Trans. Automatic Control, vol. 42, no. 7, pp. 896–
    911, July 1997.
    [67] J. Lo and M. Lin, “Robust H1 nonlinear control via fuzzy static output feedback,”
    IEEE Trans. Circuits and Syst. I: Fundamental Theory and Applications, vol. 50,
    no. 11, pp. 1494–1502, Nov. 2003
    Advisor
  • Ji-Chang Lo(羅吉昌)
  • Files
  • 953203073.pdf
  • approve in 1 year
    Date of Submission 2008-06-25

    [Back to Results | New Search]


    Browse | Search All Available ETDs

    If you have dissertation-related questions, please contact with the NCU library extension service section.
    Our service phone is (03)422-7151 Ext. 57407,E-mail is also welcomed.