On constructing single-input non-autonomous systems of full rank

Abstract

For a nonlinear system of differential equations $\dot x=f(x)$, a method of constructing a system of full rank $\dot x=f(x)+g(x)u$ is studied for vector fields of the class $C^k$, $1\le k<\infty$, in the case when $f(x)\not=0$. A method for constructing a non-autonomous system of full rank is proposed in the case when the vector field $f(x)$ can vanish.

Keywords

• nonlinear control system; accessible system; system of full rank; non-autonomous system; the straightening theorem for vector fields