  Stability perserving is an important topic in approximation of systems, e.g.\
model reduction. If the original system is stable, we often want the
approximation to be stable. But even if an algorithm preserves stability the
resulting system could be unstable in practice because of round-off errors. Our
approach is approximating this unstable reduced system by a stable system. More
precisely, we consider the following problem. Given an unstable linear
time-invariant continuous-time descriptor system with transfer function $G$,
find a stable one whose transfer function is the best approximation of $G$ in
the spaces $RH_2$ and $RH_\infty$, respectively. Explicit optimal solutions are
presented under consideration of numerical issues.
