Ljung, L., 2007, "*System Identification*", 2nd ed., Prentice Hall, New Jersey.

Gorinevsky, D., 1997, “An Approach to Parametric Nonlinear Least Square Optimization and Application to Task-Level Learning Control,” IEEE Trans. Autom. Control, 42 (7), pp. 912–927.

[CrossRef]Yurkovich, S., Tzes, A. P., Lee, I., and Hillsley, K. L., 1990, “Control and System Identification of a Two-Link Flexible Manipulator,” "*Proceedings of IEEE International Conference on Robotics and Automation*", Vol. 3 , pp. 1626–1631.

Spong, M., 1987, “Modeling and Control of Elastic Joint Robots,” ASME J. Dyn. Syst., Meas., Control, 109 , pp. 310–319.

[CrossRef]Nho, H. C., 2004, “Precise Motion Control of Flexible-Joint Robot Manipulators With an Intelligent Payload Estimator,” Ph.D. dissertation, Department of Mechanical Engineering, Purdue University, West Lafayette, IN.

Levenberg, K., 1944, “A Method for the Solution of Certain Non-Linear Problems in Least Squares,” Q. Appl. Math.,
2 , pp. 164–168.

Marquardt, D., 1963, “An Algorithm for Least Squares Estimation on Nonlinear Parameters,” SIAM J. Appl. Math., 11 , pp. 431–441.

[CrossRef]Billings, S. A., Chen, S., and Korenberg, M. J., 1989, “Identification of MIMO Non-Linear Systems Using a Forward-Regression Orthogonal Estimator,” Int. J. Control, 49 , pp. 2157–2189.

[CrossRef]Billings, S. A., and Peyton Jones, J. C., 1990, “Mapping Non-Linear Integro-Differential Equations Into the Frequency Domain,” Int. J. Control, 52 (4), pp. 863–879.

[CrossRef]Billings, S. A., and Tsang, K. M., 1989, “Spectral Analysis for Non-Linear Systems Part I: Parametric Non-Linear Spectral Analysis—Part II: Interpretation of Non-Linear Frequency Response Functions,” Mech. Syst. Signal Process., 3 , pp. 319–359.

[CrossRef]Billings, S. A., Tsang, K. M., and Tomlinson, G. R., 1990, “Spectral Analysis for Non-Linear Systems—Part III: Case Study Examples,” Mech. Syst. Signal Process., 4 , pp. 3–21.

[CrossRef]Korenberg, M., Billings, S. A., Liu, Y. P., and Mcilroy, P. J., 1987, “Orthogonal Parameter Estimation Algorithm for Non-Linear Stochastic Systems,” Int. J. Control, 48 , pp. 193–210.

[CrossRef]Leontaritis, I. J., and Billings, S. A., 1987, “Model Selection and Validation Methods for Non-Linear Systems,” Int. J. Control, 45 , pp. 311–341.

[CrossRef]Leontaritis, I. J., and Billings, S. A., 1987, “Experimental Design and Identifiability for Non-Linear Systems,” Int. J. Syst. Sci., 18 , pp. 189–202.

[CrossRef]Aguirre, L. A., and Billings, S. A., 1995, “Improved Structure Selection for Nonlinear Models Based on Term Clustering,” Int. J. Control, 62 , pp. 569–587.

[CrossRef]Aguirre, L. A., and Billings, S. A., 1995, “Dynamical Effects of Overparametrization in Nonlinear Models,” Physica D, 80 , pp. 26–40.

[CrossRef]Aguirre, L. A., and Jâcome, C. R. F., 1998, “Cluster Analysis of NARMAX Models for Signal-Dependent Systems,” IEEE Proc., Control Theory Appl., 145 , pp. 409–414.

[CrossRef]Mao, K. Z., and Billings, S. A., 1997, “Algorithms for Minimal Model Structure Detection in Nonlinear Dynamic System Identification,” Int. J. Control, 68 , pp. 311–330.

[CrossRef]Piroddi, L., and Spinelli, W., 2003, “An Identification Algorithm for Polynomial NARX Models Based on Simulation Error Minimization,” Int. J. Control, 76 (17), pp. 1767–1781.

[CrossRef]Press, W., Annery, B., Teukolsky, S., and Vetterling, W., 1992, "*Numerical Recipes in C: The Art of Scientific Computing*", 2nd ed., Cambridge University Press, Cambridge, UK.

Madsen, K., Nielsen, H. B., and Tingleff, O., 2004, "*Methods for Non-Linear Least Squares Problems*", 2nd ed., Technical University of Denmark, Lyngby, Denmark.

Mathews, J., and Fink, K., 2004, "*Numerical Methods Using MATLAB *", 4th ed., Prentice Hall, New Jersey.

Isaacson, E., and Keller, H. B., 1994, "*Analysis of Numerical Methods*", Dover Publications, New York.

Kranzer, H. C., 1963, “An Error Formula for Numerical Differentiation,” Numer. Math., 5 (1), pp. 439–442.

[CrossRef]Fornberg, B., 1981, “Numerical Differentiation of Analytic Functions,” ACM Trans. Math. Softw., 7 (4), pp. 512–526.

[CrossRef]Xian, B., de Queiroz, M. S., Dawson, D. M., and McIntyre, M. L., 2004, “A Discontinuous Output Feedback Controller and Velocity Observer for Nonlinear Mechanical Systems,” Automatica, 40 , pp. 695–700.

[CrossRef]Erlic, M., and Lu, W.-S., 1995, “A Reduced-Order Adaptive Velocity Observer for Manipulator Control,” IEEE Trans. Rob. Autom., 11 (2), pp. 293–303.

[CrossRef]
Davila, J., Fridman, L., and Levant, A., 2005, “Second-Order Sliding-Mode Observer for Mechanical Systems,” IEEE Trans. Autom. Control, 50 (11), pp. 1785–1789.

[CrossRef]Ramsay, J. O., and Silverman, B. W., 2005, "*Functional Data Analysis*", 2nd ed., Springer, New York.

Zang, Z., Bitmead, R. R., and Gevers, M, 1995, “Iterative Weighted Least-Squares Identification and Weighted LQG Control Design,” Automatica, 31 (11), pp. 1577–1594.

[CrossRef]Chatlatanagulchai, W., 2006, “Backstepping Intelligent Control Applied to a Flexible-Joint Robot Manipulator,” Ph.D. dissertation, Department of Mechanical Engineering, Purdue University, West Lafayette, IN.