Schur-Nevanlinna-Potapov sequences of rational matrix functions

We study particular sequences of rational matrix-valued functions with poles outside the unit circle. Such kind of sequences are recursively constructed based on a sequence of complex numbers with norm less than one and a sequence of strictly contractive matrices. In fact, such sequences are closely related to the so-called Schur-Nevanlinna-Potapov algorithm for matrix-valued Schur functions but also to orthogonal rational matrix-valued functions. As a main result of paper, we shall see that rational matrix-valued functions belonging to Schur-Nevanlinna-Potapov sequences can be used to parameterize the set of all solutions of an interpolation problem of Nevanlinna-Pick type for matrix-valued Schur functions