Model order reduction for a family of linear systems with applications in parametric and uncertain systems

We present an approach which creates a linear reduced order model whose transfer function interpolates at certain given points and approximates at others. We describe how to create the corresponding state space system and explain how this method is used for the simulation of large scale parametric systems or several realizations of an uncertain system. In that case, the interpolation points are the H2H2 optimal interpolation points of one particular system. The behavior of the method is illustrated in some numerical examples.