Modeling of a plant with variable operating conditions is considered. The plant is described by an interpolation of proper stable coprime factorizations of two transfer functions obtained at representative operating points. Nonlinear interpolation functions are introduced in the numerator and denominator of the interpolated model individually, which tune the interpolation parameters at reference operating points. A problem of finding suitable nonlinear interpolation functions and coprime factorizations of the transfer functions at representative operating points is formulated so that the nonlinearly interpolated model becomes the best approximation of the plant. A solution method is presented in the state space utilizing matrix inequalities.