A natural coordinate system for nonlinear systems

A natural coordinate system for nonlinear systems of the form x = f(x) + g(x)u is discussed where x is a element of R(N), u is an element of R, and f and g are analytic, vector-valued functions on R(N). It is shown that in these coordinates the equation becomes a system with only feedback paths (no feedforwards), if feedback linearizability conditions are satisfied.