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Unsolved Problems in Mathematical Systems and Control Theory by Vincent D. Blondel, Alexandre Megretski

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Problem 2.4

On the convergence of normal forms for

analytic control systems

Wei Kang

Department of Mathematics,

Naval Postgraduate School

Monterey, CA 93943

USA

wkang@nps.navy.mil

Arthur J. Krener

Department of Mathematics,

University of California

Davis, CA 95616

USA

ajkrener@ucdavis.edu

1 BACKGROUND

A fruitful technique for the local analysis of a dynamical system consists of using a local change of coordinates to transform the system to a simpler form, which is called a normal form. The qualitative behavior of the original system is equivalent to that of its normal form which may be easier to analyze. A bifurcation of a parameterized dynamics occurs when a change in the parameter leads to a change in its qualitative properties. Therefore, ...

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