A Formal Linearization for a General Class of Time-Varying Nonlinear Systems and Its Applications
Summary :
In this paper we consider an approximation method of a formal linearization which transform time-varying nonlinear systems into time-varying linear ones and its applications. This linearization is a kind of a coordinate transformation by introducing a linearizing function which consists of the Chebyshev polynomials. The nonlinear time-varying systems are approximately transformed into linear time-varying systems with respect to this linearizing functions using Chebyshev expansion to the state variable and Laguerre expansion to the time variable. As applications, nonlinear observer and filter are synthesized for time-varying nonlinear systems. Numerical experiments are included to demonstrate the validity of the linearization. The results show that the accuracy of the approximation by the linearization improves as the order of the Chebyshev and Laguerre polynomials increases.
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- IEICE TRANSACTIONS on Fundamentals Vol.E87-A No.9 pp.2203-2209
- Publication Date
- 2004/09/01
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- Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
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Kazuo KOMATSU, Hitoshi TAKATA, "A Formal Linearization for a General Class of Time-Varying Nonlinear Systems and Its Applications" in IEICE TRANSACTIONS on Fundamentals,
vol. E87-A, no. 9, pp. 2203-2209, September 2004, doi: .
Abstract: In this paper we consider an approximation method of a formal linearization which transform time-varying nonlinear systems into time-varying linear ones and its applications. This linearization is a kind of a coordinate transformation by introducing a linearizing function which consists of the Chebyshev polynomials. The nonlinear time-varying systems are approximately transformed into linear time-varying systems with respect to this linearizing functions using Chebyshev expansion to the state variable and Laguerre expansion to the time variable. As applications, nonlinear observer and filter are synthesized for time-varying nonlinear systems. Numerical experiments are included to demonstrate the validity of the linearization. The results show that the accuracy of the approximation by the linearization improves as the order of the Chebyshev and Laguerre polynomials increases.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e87-a_9_2203/_p
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@ARTICLE{e87-a_9_2203,
author={Kazuo KOMATSU, Hitoshi TAKATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Formal Linearization for a General Class of Time-Varying Nonlinear Systems and Its Applications},
year={2004},
volume={E87-A},
number={9},
pages={2203-2209},
abstract={In this paper we consider an approximation method of a formal linearization which transform time-varying nonlinear systems into time-varying linear ones and its applications. This linearization is a kind of a coordinate transformation by introducing a linearizing function which consists of the Chebyshev polynomials. The nonlinear time-varying systems are approximately transformed into linear time-varying systems with respect to this linearizing functions using Chebyshev expansion to the state variable and Laguerre expansion to the time variable. As applications, nonlinear observer and filter are synthesized for time-varying nonlinear systems. Numerical experiments are included to demonstrate the validity of the linearization. The results show that the accuracy of the approximation by the linearization improves as the order of the Chebyshev and Laguerre polynomials increases.},
keywords={},
doi={},
ISSN={},
month={September},}
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TY - JOUR
TI - A Formal Linearization for a General Class of Time-Varying Nonlinear Systems and Its Applications
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2203
EP - 2209
AU - Kazuo KOMATSU
AU - Hitoshi TAKATA
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E87-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2004
AB - In this paper we consider an approximation method of a formal linearization which transform time-varying nonlinear systems into time-varying linear ones and its applications. This linearization is a kind of a coordinate transformation by introducing a linearizing function which consists of the Chebyshev polynomials. The nonlinear time-varying systems are approximately transformed into linear time-varying systems with respect to this linearizing functions using Chebyshev expansion to the state variable and Laguerre expansion to the time variable. As applications, nonlinear observer and filter are synthesized for time-varying nonlinear systems. Numerical experiments are included to demonstrate the validity of the linearization. The results show that the accuracy of the approximation by the linearization improves as the order of the Chebyshev and Laguerre polynomials increases.
ER -
English
