On the invertibility of affine nonlinear singular control systems

This paper discusses the invertibility of affine nonlinear singular control systems. First an inversion algorithm is given for such systems, which is not only a practical procedure but also plays a very important role in studying the solvability of the inverse system. Then based on such an algorithm, a sufficient condition is derived, under which the invertibility problem for the affine nonlinear singular control systems is solvable. For invertible systems, a nonlinear inverse system is constructed. For certain noninvertible systems, the sufficient condition yields a characterization of input space on which the input-output map is inject