根據比例積分微分濾波器塑形方法，本論文提出另一適用於非極小相位非方形連續時間多變數系統之比例積分最佳線性二次式狀態估測器，結合近期被提出的最佳線性二次式追蹤器，所提出的最佳線性二次狀態估測追蹤器，對於無法量測系統之狀態且具有任意參考輸入軌跡之非極小相位非方形多變數系統，可達成類似最佳最小相位的輸出追蹤效能。本論文亦提出適用於具未知輸入干擾之連續時間最小相位系統之強健線性二次式狀態估測追蹤器，採用等效輸入干擾估測器改善其干擾抑制之效果。

Based on the proportional-integral-derivative (PID) filter shaping approach, this thesis presents an alternative proportional-plus-integral (PI) optimal linear quadratic state estimator (LQSE) for the continuous-time non-square and non-minimum phase (NMP) multivariable systems. Together with the recently developed optimal linear quadratic tracker (LQT), the proposed LQSE-based tracker is able to optimally achieve good minimum phase-like tracking performances for a non-square NMP multivariable system with unmeasurable states and arbitrary command inputs. This thesis also proposes the robust linear quadratic state-estimate tracker for continuous-time minimum phase systems with unknown input disturbance, and the proposed method improves the disturbance-rejection performance based on the estimation of an equivalent input disturbance (EID).

Anderson, B.D.O., & Mingori, D.L. (1985). Use of frequency dependence in linear quadratic problems to frequency shape robustness. Journal of Guidance and Control, 8(3), 397–401.
Anderson, B.D.O., & Moore, J.B. (1989). Optimal Control: Linear Quadratic Methods. Englewood Cliffs, NJ: Prentice-Hall.
Chen, Y.M., & Wu, Y.C. (1992). Modified recursive least-squares algorithm for parameter identification. International Journal of Systems Science, 23(2), 187–205.
Doraiswami, R., Jiang, J., & Balasubramanian, R. (1986). On-line frequency-and-time-domain identification of a linear multivariable system. International Journal of Systems Science, 17(9), 1349–1371.
Ebrahimzadeh, F., Tsai, J. S. H., Chung, M. C., Liao, Y. T., Guo, S. M., Shieh, L. S., & Wang, L. (2017a). A generalized optimal linear quadratic tracker with universal applications. Part 2: discrete-time systems. International Journal of Systems Science, 48(2), 397–416.
Ebrahimzadeh, F., Tsai, J. S. H., Liao, Y. T., Chung, M. C., Guo, S. M., Shieh, L. S., & Wang, L. (2017b). A generalized optimal linear quadratic tracker with universal applications–part 1: continuous-time systems. International Journal of Systems Science, 48(2), 376–396.
Emami-Naeini, A., & Van Dooren, P. (1982). Computation of zeros of linear multivariable systems. Automatica, 18(4), 415–430.
Latawiec, K., Banka, S., & Tokarzewski, J. (2000). Control zeros and non-minimum phase LTI MIMO systems. Annual Reviews in Control, 24(1), 105–112.
Patel, R.V., & Misra, P. (1992). Transmission zero assignment in linear multivariable systems; Part II: The general case. American Control Conference, Chicago, IL, 24-26 June, 1992, 644–648.
Ray, G., & Rama Rao, P. (1990). On-line identification and control of multivariable discrete-time systems based on a transformed model. International Journal of Systems Science, 21(1), 175–191.
She, J. H., Fang, M., Ohyama, Y., Hashimoto, H., & Wu, M. (2008). Improving disturbance-rejection performance based on an equivalent-input-disturbance approach. IEEE Transactions on Industrial Electronics, 55(1), 380–389.
Smagina, Y. (2002). Zero assignment in multivariable system using pole assignment method, available at: arXiv:math/0207094v1 [math.DS].
Syrmos, V.L., & Lewis, F.L. (1992). Transmission zero assignment using semistate descriptions. American Control Conference, Chicago, 24-26 June, 1992, 791–795.
Sebakhy, O.A., Singaby, M.EL., & Arabawy, I.F.EL. (1986). Zero placement and squaring problem: A state space approach. International Journal of Systems Science, 17(12), 1741–1750.
Sagara, S., Yang, Z.J., & Wada, K. (1991). Identification of continuous-time systems using digital low-pass filters. International Journal of Systems Science, 22(7), 1157–1176.
Tang, D., Chen, L., & Hu, E. (2014). A novel unknown-input estimator for disturbance estimation and compensation. Proceedings of Australasian Conference on Robotics and Automation, Melbourne, 2-4 Dec., 2014.
Tsai, J.S.H., Liao, Y.-T., Ebrahimzadeh, F., Lai, S.Y., Su, T.J., Guo, S.M., Shieh, L.S., & Tsai, T. J. (2017). A new PI optimal linear quadratic state-estimate tracker for continuous-time non-square non-minimum phase systems, International Journal of Systems Science, 48(7), 1438–1459.
Trinh, H., Fernando, T., & Nahavandi, S. (2004). Design of reduced-order functional observers for linear systems with unknown inputs. Asian Journal of Control, 6(4), 514–520, doi:10.1111/j.1934-6093.2004.tb00372.x
Wu, W.T., Tseng, C.G., & Chu, Y.T. (1994). System identification and on-line robust control of a multivariable system. International Journal of Systems Science, 25(3), 423–439.
Zheng, W.X. (2006). Least squares parameter estimation of linear systems with noisy input-output data. International Journal of Systems Science, 37(7), 447–453.