Coprime factorizations of nonlinear and time-varying systems

The author develops the notion of coprimeness for nonlinear systems from an input-output viewpoint and shows it to be equivalent to the usual notion of coprimeness for FDLTI (finite-dimensional linear time-invariant) systems. He considers the role of right coprime fractional representations for nonlinear systems in representing the stable input-output behavior of possibly unstable nonlinear systems. Using this notion of coprimeness, he obtains a criterion for the stability of nonlinear feedback systems in terms of the right coprime fractional representations of the plant and the controller. He also obtains a parametrization of all nonlinear time-varying stabilizing controllers for linear (possibly time-varying) plants that has the same form as the familiar Youla parameterization of all FDLTI stabilizing controllers for FDLTI plants