Strongly Structural Input and State Observability for Linear Time Invariant Network Systems

This paper considers linear discrete-time network systems affected by unknown Inputs, studying whether they are input and state observable (ISO), namely whether both the initial state and the unknown input can be reconstructed from the output measurements. More precisely, the paper studies ISO, where the input reconstruction must happen with at most one time-step delay, and unconstrained ISO, where a larger delay is allowed. The focus is on strongly structured (unconstrained) ISO, wherein the objective is to find conditions such that for all system matrices that share a given zero/non-zero pattern, the resulting system is (unconstrained) ISO. We first provide a graphical characterization for strongly structural unconstrained ISO. Then, we find a sufficient condition and a necessary condition for strongly structural ISO, which are equivalent in the case without direct feedthrough. All conditions are in terms of existence of suitable uniquely restricted matchings in bipartite graphs associated with the system.