Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31097
Design of Nonlinear Observer by Using Augmented Linear System based on Formal Linearization of Polynomial Type

Authors: Kazuo Komatsu, Hitoshi Takata


The objective of this study is to propose an observer design for nonlinear systems by using an augmented linear system derived by application of a formal linearization method. A given nonlinear differential equation is linearized by the formal linearization method which is based on Taylor expansion considering up to the higher order terms, and a measurement equation is transformed into an augmented linear one. To this augmented dimensional linear system, a linear estimation theory is applied and a nonlinear observer is derived. As an application of this method, an estimation problem of transient state of electric power systems is studied, and its numerical experiments indicate that this observer design shows remarkable performances for nonlinear systems.

Keywords: Electric Power System, Nonlinear System, augmented linear system, nonlinear observer, formal linearization

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1270


[1] A. J. Krener, "Approximate Linearization by State Feedback and Coordinate Change," Systems and Control Letters, Vol.5, pp.181-185, 1984.
[2] R. Marino, "On the Largest Feedback Linearizable Subsystem," Systems and Control Letters, Vol.6, pp.345-351, 1986.
[3] W. T. Baumann and W. J. Rugh, "Feedback Control of Nonlinear Systems by Extended Linearization," IEEE Trans., AC-31, 1, pp.40-46, 1986.
[4] R. R. Kadiyala, "A Tool Box for Approximate Linearization on Nonlinear Systems," IEEE Control Systems, Vol.13, No.2, pp.47-57, 1993.
[5] A. Ishidori, Nonlinear Control Systems II , Springer-Verlag, London, 1999.
[6] H. K. Khalil, Nonlinear Systems, 3rd ed., New Jersey: Prentice Hall, 2002.
[7] H. Takata," Transformation of a Nonlinear System into an Augmented Linear System," IEEE Trans. on Automatic Control, Vol.AC-24, No.5, pp.736-741, 1979.
[8] K. Komatsu and H. Takata, "Design of Time-Delay Nonlinear Observer by Using a Formal Linearization," in Proc. of RISP International Workshop on Nonlinear Circuits and Signal Processing(NCSP-07), Shanghai, China, pp.137-140, 2007.
[9] G. W. Johnson, "A Deterministic Theory of Estimation and Control," IEEE Trans. on Automatic Control, pp. 380-384, 1969.
[10] A. P. Sage and C. C. White III, Optimum Systems Control, 2nd ed., Prentice-Hall,Inc., 1977.