## A canonical expansion for nonlinear systems.(English)Zbl 0618.93028

In the first part of the paper the authors consider n vector fields $$X_ 1,...,X_ n$$ which are linear independent and analytic in a neighborhood of the origin of $${\mathbb{R}}^ n$$. A local coordinate system based on $$X_ 1,...,X_ n$$ is constructed, and it is shown that in this coordinate system each analytic vector field has a series expansion whose coefficients are computed in terms of Lie brackets.
In the second part, the authors apply this result to control systems of the form $\dot x=f(x)+\sum^{m}_{i=1}g_ i(x)u_ i$ which satisfy suitable assumptions. The resulting expansion allows us to find out the feedback linearizable part of the given system.
Reviewer: A.Bacciotti

### MSC:

 93C10 Nonlinear systems in control theory 57R27 Controllability of vector fields on $$C^\infty$$ and real-analytic manifolds 93B27 Geometric methods 41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) 93C15 Control/observation systems governed by ordinary differential equations

### Keywords:

vector fields; series expansion; Lie brackets
Full Text: