Ill-posed distributed parameter systems: a control viewpoint

The use of linear time-invariant distributed parameter systems (LTIDPSs) as models of physical processes is considered from a control viewpoint. Specifically, classes of LTIDPSs exhibiting properties which potentially limit their usefulness in feedback design are defined and termed ill-posed. The structure of these classes is investigated within a general mathematical framework which encompasses many distributed parameter systems of engineering interest. Within this framework necessary and sufficient conditions are derived which completely characterize these classes and establish their equivalence