MIMO LTI系統的regulation已是習用技術，即使系統含有未知項，也有諸多策略可達到控制目的。但是，該類系統的追蹤問題，除了特殊方法外，文獻中並未見到廣泛的探討；一旦同時考量未知項的影響，其在文獻中幾乎絕蹤。本文針對含有匹配式干擾之MIMO LTI系統的追跡問題，提出一強健追蹤控制器，其中利用極點配置法，來安排閉迴路系統的動態行為；再用滑動控制，以解決不確定項的影響。推導過程以Lyapunov理論來確保追蹤誤差的漸進收斂性，並透過電腦模擬，來驗證本文所提控制器的可行性。

The regulation of MIMO LTI systems is a well-known technique even for the systems with various uncertainties. However, except for some special strategies, the tracking problem attracts much less attention in the literature. This thesis presents a solution to the robust tracking problem for MIMO LTI systems with matched uncertainties. The pole placement state feedback controller is utilized to give a proper closed loop dynamics, while the sliding control design is employed to provide robust effort to tolerate the uncertainties. The closed loop stability is justified by the Lyapunov theory via rigorous mathematical derivations. Computer simulations are performed to show the efficacy of the proposed scheme.

[1] J.-J. E. Slotine and W. Li, Applied nonlinear control, Prentice Hall, Englewood Cliffs, NJ, 1991.
[2] R. L. Williams and D. A. Lawrence, Linear state-space control systems, John Wiley & Sons, 2007.
[3] B. C. Kuo and F. Golnaraghi, Automatic Control Systems, 8th ed., Wiley, 2002.
[4] N. S. Nise, Control system engineering, John Wiley & Sons, 2011.
[5] D. Xue, Y. Q. Chen, and D. P. Atherton, Linear feedback control: analysis and design with MATLAB, Society for Industrial and Applied Mathematics, 2007.
[6] P. A. Ioannou and J. Sun, Robust adaptive control, Prentice Hall, 2012.
[7] V. Utkin, “Variable structure systems with sliding modes,” IEEE Transactions on Automatic Control, vol. 22, pp. 212-222, 1977.
[8] C. Edwards and S. Spurgeon, Sliding mode control: theory and applications, CRC Press, 1998.
[9] S. Gutman and G. Leitmann, “Stabilizing control for linear systems with bounded parameter and input uncertainty,” IFIP Conference on Optimization Techniques, pp. 729-755, 1975.
[10] S. Gutman and G. Leitmann, “Stabilizing feedback control for dynamical systems with bounded uncertainty,” IEEE Conference on Decision and Control, pp. 94-99, 1976.
[11] S. Gutman, and G. Leitmann, “On a class of linear differential games,” Journal of Optimization Theory and Applications, vol. 17, no. 5-6, pp. 511-522, 1975.
[12] G. Leitmann, “Guaranteed asymptotic stability for some linear systems with bounded uncertainties” Journal of Dynamic Systems, Measurement, and Control, vol. 101, pp. 212-216, 1979.
[13] S. Gutman, “Uncertain dynamical systems--A Lyapunov min-max approach,” IEEE Transactions on Automatic Control, vol. 24, no. 3, pp. 437-443, 1979.
[14] M. Corless and G. Leitmann, “Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems,” IEEE Transactions on Automatic Control, vol. 26, pp.1139-1144, 1981.
[15] B. R. Barmish, M. Corless, and G. Leitmann, “A new class of stabilizing controllers for uncertain dynamical systems,” SIAM Journal on Control and Optimization, vol. 21, pp. 246-255, 1983.
[16] Y. H. Chen and G. Leitmann, “Robustness of uncertain systems in the absence of matching assumptions,” International Journal of Control, vol. 45, no. 5, pp. 1527-1542, 1987.
[17] W. E. Schmitendorf and T. H. Hopp, “Asymptotic tracking of uncertain systems in the absence of matching conditions,” American Control Conference, pp. 423-426, 1985.
[18] W. E. Schmitendorf, “Methods for obtaining robust tracking control laws,” American Control Conference, pp. 212-216, 1986.
[19] W. E. Schmitendorf, “Stabilizing controllers for uncertain linear systems with additive disturbances,” International Journal of Control, vol. 47, no. 1, pp. 85-95, 1988.
[20] Z. Qu and D. M. Dawson, “Continuous state feedback control guaranteeing exponential stability for uncertain dynamical systems,” IEEE Conference on Decision and Control, pp. 2636-2638, 1991.
[21] H. Wu, K. Mizukami, and C. Letters, “Exponential stability of a class of nonlinear dynamical systems with uncertainties,” Systems & Control Letters, vol. 21, no. 4, pp. 307-313, 1993.
[22] G. Tao, Adaptive control design and analysis, John Wiley & Sons, 2003.
[23] B. Xian, D. M. Dawson, M. S. de Queiroz, and J. Chen, “A continuous asymptotic tracking control strategy for uncertain nonlinear systems,” IEEE Transactions on Automatic Control, vol. 49, no. 7, pp. 1206-1211, 2004.
[24] J. Chen, A. Behal, and D. M. Dawson, “Robust feedback control for a class of uncertain MIMO nonlinear systems,” IEEE Transactions on Automatic Control, vol. 53, no. 2, pp. 591-596, 2008.
[25] S. Mobayen, M. H. Asemani, and V. J. Majd, “Transient performance improvement using composite nonlinear feedback and integral sliding surface for matched and unmatched uncertain MIMO linear systems,” The 3rd International Conference on Control, Instrumentation, and Automation, pp. 83-88, 2013.
[26] 楊育瑋，多輸入多輸出線性系統之滑動追蹤控制器設計，碩士論文，機械工程系，國立臺灣科技大學，2019。