Invertibility of multivariable nonlinear control systems

This paper gives sufficient conditions for the invertibility of nonlinear control systems of the form
\dot{x}= A(x)+ u_{1}B_{1}(x) +... + u_{m} B_{m}(x);y=c(x)
, where the state space is a real analytic manifold. These conditions are also necessary in the case of single-input nonlinear systems and multivariable time-invariant linear systems. For invertible systems we construct nonlinear inverse systems.