Null/Pole Interpolation Problem in the Class $$\mathcal {RI}$$ RI of Rational Functions Intertwining Solutions of Linear Differential Equations

Abstract

We formulate and solve the null/pole interpolation problem for the class \({\varvec{\mathcal {RI}}}\) of rational matrix-valued functions intertwining solutions of linear ODEs with a spectral parameter; such functions appear naturally as transfer functions of overdetermined 2D systems invariant in one direction. The salient new feature, as compared to the usual null/pole interpolation problem for rational matrix-valued functions, is that the null and pole vectors are replaced by the null and pole solutions of the given ODEs for the values of the spectral parameter equal to the prescribed zeroes and poles. As a byproduct we obtain a realization theorem and a Hermitian (conservative) realization theorem.