The fractional representations of a class of nonlinear systems

Abstract

Right and left coprime fractional representations are shown to exist for a special class of nonlinear systems that have both controller and observer forms. A generalized Bezout identity is given for this class of nonlinear systems. Using the controller form, it is possible to design a nonlinear feedback controller. The given system can be right factorized into a composite of a stable postprocessor and an inverse of a stable preprocessor. The right-coprimeness concept is based on this right factorization. When the postprocessor and preprocessor are combined, they form a higher dimensional system. The existence of a stable left inverse of this higher order system constitutes the authors' definition of right coprimeness.