Observability theorems for some linear hyperbolic systems

In this paper the observability of systems of first-order hyperbolic partial differential equations is investigated. Both systems with boundary measurements and systems with distributed measurements are considered. In the case of boundary measurements a sufficient condition is found for observability. This condition is shown also to be necessary for systems defined on a one-dimensional space domain, as well as in other special cases. In the case of linear distributed measurements, a necessary and sufficient condition for observability is derived. The theorems are applicable for example to linearized hydrodynamical flow equations and to industrial flow system equations.