近幾年來，對於分子運動的最佳化控制以及閉迴路控制，已經有相當多的研究及成果，但是並未有利用LMI (Linear Matrix Inequality)控制理論來設計分子運動的強健控制器之相關的研究。本論文目的在於設計分子運動的強健控制器，文中將分子運動取其期望值，利用古典力學方式為分子運動系統建模。在假設系統狀態為可量測的狀況下，針對系統的不確定性來設計H∞、H2、以及混合控制器，並利用Matlab軟體中的LMI toolbox模擬設計結果，並針對不同控制器在不同系統條件下的性能作比較。

　In recent years there is a great deal of effort made on the optimal and feedback control of the molecular system. But no studies have ever been tried to control the molecular motion with the LMI (Linear Matrix Inequality) control theory. In this thesis, we propose a LMI-based robust controller for the molecular motion system. Taking the expectation of molecular motion, we can derive a classical equation of motion from which, we then design H2,H∞ and H2/H∞、 controller for molecular systems with certainty. Finally, we use the LMI toolbox in matlab to simulate the result, and compare the performance of different control designs under different excitation conditions.

參考文獻
[1] G. M. Huang, T. J. Tarn, “ On the controllability of quantum- mechanical systems” Journal of Mathematics and Physics, 1983.11,24(11): 2608-2618
[2] C. K. Ong, G. M. Huang, T. J. Tarn, J. W. Clark,”Inver- tibility of Quantum-Mechanical Control Systems,Math-
ematical Systems Theory”, 1984, 17:335-350
[3] A. P. Peirce, M. A. Dahleh, H. Rabitz, “Optimal control of quantum-mechanical systems: Existence, numerical app- roximation, and applications”, Phys. Rev. A, vol. 37, pp. 4950-4964, 1998
[4] W. S. Warren, H. Rabitz, M. Dahleh, “Coherent Control of Quantum Dynamics: The Dream Is Alive”, Science, 1993.3, 259(12):1581-1585
[5] R. S. Judson, H. Rabitz, “Teaching laser to control mo- lecules”, Phys. Rev. Lett., vol.68, pp. 1500-1503,1992
[6] A. C. Doherty, S. M. Tan, A. S. Parkins, D. F. Walls, “State determination in continuous measurement”, Phys. Rev. A, 60, 21384, 1999
[7] A. C. Doherty, K. Jacobs, “Feedback-control of quantum systems using continuous state-estimation”, Phys. Rev. A, 60, 2700, 1999
[8] M. Yanagisawa, H. Kimura, “Transfer function approach to quantum control part I: Dynamics of Quantum Feedback Sy- stem ”, IEEE Trans. Automat. Contr., vol. 48, pp.2104- 2120, Dec, 2003
[9] M. Yanagisawa, H. Kimura,“Transfer function approach to quantum control part II: Control Concepts and Applicat- ions”, IEEE Trans. Automat. Contr., vol. 48, Dec, 2003
[10] H. Zhang, H. Rabitz, “Robust optimal control of quantum molecular systems in the presence of disturbances and uncertainties”, Phys. Rev. A, vol.49, 4,1994
[11] C. Ahn, A. C. Doherty, A. J. Landhl, “Continuous quantum error correction via quantum feedback control”, Phys. Rev. A, vol.65, 042301, 2002
[12] J. k. Stockton, J. M. Geremia, A. C. Doherty, H. Mabuchi, “Robust quantum parameter estimation: Coherent magnet-
ometry with feedback ”, Phys. Rev. A, vol.69, 032109, 2004
[13] 孫允平,”高速鐵路列車巡弋控制及衛星姿態控制-混和 / 設計法”, 2001, 成大航太所博士論文
[14] H.M. Wiseman and G.J. Milburn, Phys. Rev. Lett. 70, 548 (1993); H.M. Wiseman, Phys. Rev. A 49, 2133 (1994); 49, 5159(E) (1994); 50, 4228(E) (1994).