A new parametrization of rational inner functions of fixed degree: Schur parameters and realizations

We present a new parametrization of inner functions based on the Schur algo rithm. We make use of state space formulas (in practice we obtain a new par ametrization of observable pairs). The main advantage of our parametrizatio n is that for each chart the observability gramian is constant: this leads to very good behavior in some approximation problems.