  We present a framework for constructing structured realizations of linear
dynamical systems having transfer functions of the form $C(\sum_{k=1}^K
h_k(s)A_k)^{-1}B$ where $h_1,h_2,\ldots,h_K$ are prescribed functions that
specify the surmised structure of the model. Our construction is data-driven in
the sense that an interpolant is derived entirely from measurements of a
transfer function. Our approach extends the Loewner realization framework to
more general system structure that includes second-order (and higher) systems
as well as systems with internal delays. Numerical examples demonstrate the
advantages of this approach.
