Geometrically Constrained Observability

This paper deals with observed processes in situations in which observations are available only when the state vector lies in certain regions. For linear autonomous observed processes, necessary and sufficient conditions are obtained for half space observation regions. These results are shown to contain a theorem dual to a controllability result proved by the author for a linear autonomous control system whose control restraint set does not contain the origin as an interior point. Observability results relating to continuous observation systems and sampled data systems are presented, and an example of observing the state of an electrical network is given.