本篇論文解決大型線性系統分散式穩定與成本控制問題。其中，大型系統是由數個子系統所結合而成，並且利用Takagi-Sugeno (T-S)模糊模型來表示。而兩個子系統互相連結的方式是以線性連結或是滿足相稱的非線性項連結。本文中，係利用平行分配補償(Parallel Distributed Compensation)來設計分散式糊模控制器。本文的主要貢獻有 (一)利用李亞普諾夫(Lyapunov)法則及瑞卡地(Riccate)不等式，提出對於模糊大型系統的穩定條件，並且滿足系統的相稱非線性連結限制。 (二)對於以線性連結的T-S模糊大型系統，提出兩個穩定條件。第一種條件是利用兩條不等式去滿足每個子系統，使整個大型系統漸近穩定。第二種條件是利用一個大型負定矩陣，一次就滿足整個大型系統漸近穩定；而大型矩陣當中包含了每個子系統與子系統的互相連結項。 (三)對於模糊大型系統的成本控制與穩定條件，我們也將討論，並且提出充分條件同時達成以上兩項目的。 (四)每一章所提出的控制方法或條件，我們都將以數值的例子或實際例子，利用線性矩陣不等式(Linear Matrix Inequality)求解，來實現並驗證其效能。

This dissertation studies the stabilization and decentralized guaranteed cost control problem for a large-scale system. The considered large-scale system is composed of several number of subsystems and each subsystem is represented by a Takagi-Sugeno (T-S) fuzzy model. The interconnection between any two subsystems may be linear or nonlinear with satisfies some matching condition. In each chapter, the decentralized fuzzy control by the concept of parallel distributed compensation (PDC) for each subsystem is synthesized. Based on Lyapunov criterion, some sufficient conditions are derived and the common and local state feedback gain are solved by linear matrix inequalities (LMIs) so that the whole closed-loop large-scale fuzzy system with the synthesized fuzzy control is asymptotically stable and cost control is guaranteed, respectively. In each chapter, a numerical or practical example is given to illustrate the control synthesis and its effectiveness.

[1] M. Akar and Ü. Özgüner, “Decentralized techniques for the analysis and control of Takagi-Sugeno fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 8, no. 6, pp. 691-704, 2000.
[2] J.J. Buckley, “Universal fuzzy controllers,” Automatica, vol. 28, pp. 1245-1248, 1992.
[3] Y. Y. Cao and P. M. Frank, “Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach,” IEEE Transactions on Fuzzy Systems, vol. 8, no. 2, pp. 200–211, Apr. 2000.
[4] B. S. Chen and W. J. Wang, “Robust stabilization of nonlinearly perturbed large-scale systems by decentralized observer-controller compensators,” Automatica, vol. 26, pp. 1035-1041, 1990.
[5] B. Chen and X. Liu, “Fuzzy guaranteed cost control for nonlinear systems with time-varying delay,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 2, pp. 238-249, April 2005.
[6] C. F. Cheng, “Design of robust observation schemes for uncertain large scale systems,” IEE Proceedings Control Theory and Applications, vol. 144, no. 5, pp. 369-374, 1997.
[7] C. F. Cheng, W. J. Wang, and Y. P. Lin, “Decentralized controller design for large-scale systems,” International Journal of Systems Science, vol. 25, no. 1, pp. 83-95, 1994.
[8] C. C. Chiang and Z. H. Kuo, “Decentralized adaptive fuzzy controller design of large-scale nonlinear systems with unmatched uncertainties,” in The 11th IEEE Conference on Fuzzy Systems, vol. 1, pp. 668-673, 2002.
[9] C. H. Chou and C. C. Cheng, “A decentralized model reference adaptive variable structure controller for large-scale time-varying delay systems,” IEEE Transactions on Automatic Control, vol. 48, no. 7, pp. 1213-1217, July 2003.
[10] F. Da, “Decentralized sliding mode adaptive controller design based on fuzzy neural networks for interconnected uncertain nonlinear systems,” IEEE Transactions on Neural Networks, vol. 11, no. 6, pp. 1471-1480, Nov. 2000.
[11] Z. Gong, “Decentralized robust control of uncertain interconnected systems with prescribed degree of exponential convergence,” IEEE Transactions on Automatic Control, vol. 40, no. 4, pp. 704-707, 1995.
[12] Z. H. Guan, Y. Q. Liu, and X. C. Wen, “Decentralized stabilization of singular and time-delay large-scale control systems with impulsive solutions,” IEEE Transactions on Automatic Control, vol. 40, no. 8, pp. 1437-1441, 1995.
[13] X. P. Guan and C. L. Chen, “Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays,” IEEE Transactions on Fuzzy Systems, vol. 12, no. 2, pp. 236-249, April 2004.
[14] J. Hale, Theory of Functional Differential Equations, Springer, New York, 1977.
[15] F. H. Hsiao and J. D. Hwang, “Stability analysis of fuzzy large-scale systems,” IEEE Transactions on Systems, Man, Cybernetics, Part B, vol. 32, no. 1, pp. 122-126, 2002.
[16] F. H. Hsiao, J. D. Hwang, C. W. Chen, and Z. R. Tsai, “Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 1, pp. 152-163, Feb. 2005.
[17] F. H. Hsiao, J. D. Hwang, and L. G. Shiau, “Decentralized stabilization of fuzzy large-scale systems,” Proceedings of the 39th IEEE Conference on Decision and Control, pp.3447-3452, 2000.
[18] Z. P. Jiang, “Decentralized and adaptive nonlinear tracking of large-scale systems via output feedback,” IEEE Transactions on Automatic Control, vol. 45, no. 11, pp. 2122–2128, Nov. 2000.
[19] Z. P. Jiang, D. W. Repperger, and D. J. Hill, “Decentralized nonlinear output-feedback stabilization with disturbance attenuation,” IEEE Transactions on Automatic Control, vol. 46, no. 10, pp. 1623-1629, 2001.
[20] B. Labibi, B. Lohmann, A. K. Sedigh, and P. J. Maralani, “Sufficient condition for stability of decentralised control,” Electronics Letters, vol. 36, no. 6, pp.588-590, 2000.
[21] P. L. Liu and T. J. Su, “Stability for single and large-scale uncertain systems with time-varying delays,” IEE Proceedings Control Theory and Applications, vol. 146, no. 6, pp. 591-597, 1999.
[22] X. Liu and Q. Zhang, “Approaches to quadratic stability conditions and control designs for T-S fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 11, no. 6, pp. 830-839, Dec. 2003.
[23] A. N. Michel and R. K. Miller, Qualitative Analysis of Large Scale System. Academic Press: New York, 1977.
[24] H. Mukaidani, “An LMI approach to decentralized guaranteed cost control for a uncertain nonlinear large-scale delay systems,” Journal of Mathematical Analysis and Applications, vol. 300, no. 1, pp. 17-29, 2004.
[25] K. K. Shyu, W. J. Liu, and K. C. Hsu, “Decentralised variable structure control of uncertain large-scale systems containing a dead-zone,” IEE Proceedings Control Theory and Applications, vol. 150, no. 5, pp. 467-475, Sep. 2003.
[26] D. D. Siljak, Large-Scale Dynamic Systems: Stability and Structure, North-Holland 1978, pp. 366-367.
[27] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Transactions on Systems, Man, Cybernetics, vol. SMC-15, pp. 116-132, Jan./Feb. 1985.
[28] K. Tanaka and M. Sugeno, “Stability analysis and design of fuzzy control systems,” Fuzzy Sets and Systems, vol. 45, pp. 135-156, 1992.
[29] K. Tanaka, T. Ikede, and H. O. Wang, “Design of fuzzy control systems based on relaxed LMI stability condition,” Proceedings of the 35th IEEE Conference on Decision and Control, pp. 598-603, 1996.
[30] H. Trinh and M. Aldeeh, “Distributed state observer scheme for large-scale interconnected systems,” IEE Proceedings Control Theory and Applications, vol. 145, no. 3, pp.331-337, 1998.
[31] J. T. Tsay, P. L. Liu, and T. J. Su, “Robust stability for perturbed large-scale time-delay systems,” IEE Proceedings Control Theory and Applications, vol. 143, no. 3, pp. 233-236, 1996.
[32] C. S. Tseng and B. S. Chen, “ decentralized fuzzy model reference tracking control design for nonlinear interconnected systems,” IEEE Transactions on Fuzzy Systems, vol. 9, no. 6, pp. 795-809, 2001.
[33] H. O. Wang, K. Tanaka, and M. F. Griffin “An approach to fuzzy control of nonlinear systems: stability and design issues,” IEEE Transactions on Fuzzy Systems, vol. 4, no. 1, pp. 14-23, 1996.
[34] L. X. Wang, “Fuzzy systems are universal approximators,” in First IEEE International Conference on Fuzzy Systems, pp. 1163-1170, 1992.
[35] R. J. Wang, “Nonlinear decentralized state feedback controller for uncertain fuzzy time-delay interconnected systems,” Fuzzy Sets and Systems, vol. 151, no. 1, pp. 191-204, 2005.
[36] R. J. Wang and W. J. Wang, “Fuzzy control design for perturbed fuzzy time-delay large-scale systems,” The IEEE International Conference on Fuzzy Systems, pp. 537-542, 2003.
[37] W. J. Wang and C. F. Cheng, “Robustness of perturbed large-scale systems with local constant state feedback,” International Journal of Control, vol. 50, no. 1, pp. 373-384, 1989.
[38] W. J. Wang, C. C. Kao, and C. S. Chen, “Stabilization, estimation and robustness for large-scale time-delay systems,” Control-Theory and Advanced Technology, vol. 7, pp. 569-585, Dec. 1991.
[39] W. J. Wang and L. G. Mau, “Stabilization and estimation for perturbed discrete time-delay large-scale systems,” IEEE Transactions on Automatic Control, vol. 42, no. 9, pp.1277-1282, 1997.
[40] W. J. Wang and L. Luoh, “Stability and stabilization of fuzzy large-scale systems,” IEEE Transactions on Fuzzy Systems, vol. 12, no. 3, pp. 309-315, June 2004.
[41] W. J. Wang, C. C. Song, and C. C. Kao, “Robustness bounds for large-scale time-delay systems with structured and unstructured uncertainties,” International Journal of Systems Science, vol. 22, no. 1, pp. 209-216, 1991.
[42] W. J. Wang and W. W. Lin, “Decentralized PDC for large-scale T-S fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 6, pp. 779-786, Dec. 2005.
[43] Y. Wang and Q. L. Zhang, “Robust fuzzy decentralized control for nonlinear interconnected descriptor,” 2001 IEEE International Fuzzy Systems conference, pp. 1392-1395, 2001.
[44] H. Wu, “Decentralized adaptive robust control for a class of large-scale systems including delayed state perturbations in the interconnections,” IEEE Transactions on Automatic Control, vol. 47, no. 10, pp.1745-1751, 2002.
[45] B. Xu, “On delay-independent stability of large-scale systems with time delays,” IEEE Transactions on Automatic Control, vol. 40, no. 5, pp.930-933, 1995.
[46] G. Zhai, K. Yasuda, and M. Ikeda, “Decentralized quadratic stabilization of large-scale systems,” Proceedings of the 33rd IEEE Conference on Decision and Control, pp. 2337-2339, 1994.