  Infinite-dimensional linear systems with unbounded input and output operators
are considered. For the purpose of finite-dimensional observer-based state
feedback, an observer approximation scheme will be developed which can be
directly combined with existing late-lumping controllers and observer output
injection gains. It relies on a decomposition of the feedback gain, resp.
observer output injection gain, into a bounded and an unbounded part. Based on
a perturbation result, the spectrum-determined growth condition is established,
for the closed loop.
