H-infinity norm for a control system is more than merely being a norm on the operator that maps the input space to the output space. Quite often it is also a measure to assess how robustly stable the control system is, knowledge of which is invaluable in the presence of uncertainty. We deal with control systems with large order, for such we tailor subspace frameworks that enable us to compute their H-infinity norms. Our approach in the end is based on Petrov-Galerkin projections of the large-scale systems onto carefully constructed small subspaces so that Hermite interpolation properties hold between the large-scale and projected systems. The last part of the talk extends the subspace framework to compute the stability radii of a linear dissipative Hamiltonian (DH) system, a structured control system stable in the Lyapunov sense, but that can become unstable due to unstructured perturbations. As a real application, we consider the stability radii of DH systems that arise from finite element models of disk brakes.