A Formal Linearization for a General Class of Time-Varying Nonlinear Systems and Its Applications

Kazuo KOMATSU  Hitoshi TAKATA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A   No.9   pp.2203-2209
Publication Date: 2004/09/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
formal linearization,  time-varying nonlinear system,  nonlinear observer,  nonlinear filter,  

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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.