Spectral Assignability of Systems with Scalar Control and Application to a Degenerate Hyperbolic System

Some distributed parameter systems with solar 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 be approximately controllable and that feedback relations of a certain type be continuous. We show that these conditions are satisfied by systems that are exactly controllable. We then apply the general results to a degenerate hyperbolic system. Having shown that it is exactly controllable, we obtain a spectral assignability result. Finally, we consider systems that may have multiple eigenvalues.