Spectral assignability of systems with scalar control and application to a degenerate hyperbolic system

Some distributed paramater systems with scalar boundary control can be represented as systems in Hilbert spaces for which the input functional may not be continuous, but are admissible in some sense. We prove a spectral assignability result for such systems. The conditions we need are that the system should be approximately controllable and that feedback relations of a certain type are continuous. We show that these conditions are satisfied by systems that are exactly controllable. We then apply the general results to a degenerate hyperbolec system. Having shown that it is exactly controllable, we obtain a spectral assignability result.