  Optimal model reduction for large-scale linear dynamical systems is studied.
In contrast to most existing works, the systems under consideration are not
required to be stable, neither in discrete nor in continuous time. As a
consequence, the underlying rational transfer functions are allowed to have
poles in general domains in the complex plane. In particular, this covers the
case of specific conservative partial differential equations such as the linear
Schr\"odinger and the undamped linear wave equation with spectra on the
imaginary axis. By an appropriate modification of the classical continuous time
Hardy space $\mathcal{H}_2$, a new $\mathcal{H}_2$ like optimal model reduction
problem is introduced and first order optimality conditions are derived. As in
the classical $\mathcal{H}_2$ case, these conditions exhibit a rational Hermite
interpolation structure for which an iterative model reduction algorithm is
proposed. Numerical examples demonstrate the effectiveness of the new method.
