Coprime fractional representations of nonlinear systems

Fractional representation methods for finite-dimensional linear time-invariant (FDLTI) systems have been developed in an algebraic framework of principal ideal domains. Generalizations of these methods to nonlinear systems focus on the role of Bezout identities in defining and using such representations. The author examines the role of right coprime fractional representations of a nonlinear system in representing the set of all stable input-output pairs of the system. This notion of coprimeness is equivalent to the usual notion of coprimeness for FDLTI systems. Using coprime fractional representations, the author obtains a characterization of the stability of nonlinear feedback systems and a parameterization of all nonlinear and time-varying stabilizing controllers for linear (possibly time-varying) plants