Invertibility of Nonlinear Control Systems

This paper gives necessary and sufficient conditions for the invertibility of nonlinear control systems of the form x = A(x) + uB(x); $y = c(x)$, where the state space is a real analytic manifold. For invertible systems we construct nonlinear inverse systems. These results are used to study the question of functional controllability for nonlinear systems. The class of real analytic functions which can appear as outputs of a given nonlinear system is described, and a prefilter is constructed to generate the required control.