Data Informativity for Observability: An Invariance-based Approach

Observability is a central concept within systems and control. In particular, many solutions to control problems have observability as a prerequisite. This paper is interested in characterizing observability in the case where the system is not fully known, but where state measurements are available only. As these measurements may not uniquely determine the system, we provide necessary and sufficient conditions under which all systems consistent with the measurements are observable.