[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 1322 times. Download 420 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82Reference [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. 2003Advisor Ji-Chang Lo(羅吉昌)

Files approve in 1 year

953203073.pdf Date of Submission 2008-06-25

Our service phone is (03)422-7151 Ext. 57407,E-mail is also welcomed.