Fliess series, a generalization of the Ree's theorem, and an algebraic approach to a homogeneous approximation problem

Abstract

In this paper, an algebraic technique originated by M. Fliess is developed and applied to a homogeneous approximation problem for nonlinear affine control systems. The central role is played by a generalization of the R. Ree's theorem on a connection of Lie elements and the shuffle product operation in a free associative algebra.

Acknowledgments

The authors would like to express their gratitude to the editor and the anonymous referees for their remarks and advices.