MATHEMATICA BOHEMICA, Vol. 121, No. 3, pp. 225-248, 1996

Decoupling normalizing transformations and local stabilization of nonlinear systems

S. Nikitin

S. Nikitin, Department of Mathematics, Arizona State University, Tempe, Arizona, AZ-85287-1804, USA, e-mail: nikitin@lagrange.la.asu.edu, http://lagrange.la.asu.edu

Abstract: The existence of the normalizing transformation completely decoupling the stable dynamic from the center manifold dynamic is proved. A numerical procedure for the calculation of the asymptotic series for the decoupling normalizing transformation is proposed. The developed method is especially important for the perturbation theory of center manifold and, in particular, for the local stabilization theory. In the paper some sufficient conditions for local stabilization are given.

Keywords: nonlinear system, stabilization, center manifold, normalizing transformation, smooth feedback

Classification (MSC91): 34A34, 34D05, 34D35, 93C10, 93D15

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