Total and partial observation–detection in linear dynamical systems with characterized sources: finite-dimensional cases
In this work, we address the partial observation–detection problem for finite-dimensional dynamical linear systems that may not be fully observable or detectable. We introduce the concepts of `observation–detection' and `partial observation–detection,' which involve reconstructing either the entirety or a portion of the system state and the source reacting on the system, even when the system is not fully observable or detectable. We provide characterizations of `observable–detectable systems' and `observable–detectable spaces.' The reconstruction of the state and sou