On the closest stable descriptor system in the respective spaces RH2 and RH∞

We consider the following approximation 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 RH2 and RH∞, respectively. Explicit optimal solutions are presented under consideration of numerical issues. An application in the field of stability preserving model reduction is illustrated by some examples.