Structural and Strongly Structural Input and State Observability of Linear Network Systems

This paper studies linear network systems affected by multiple unknown inputs with the objective of reconstructing both the initial state and the unknown input with one time-step delay. We state conditions under which both the whole network state and the unknown input can be reconstructed from output measurements, over every window of length N, with N being the dimension of the system, for all system matrices that share a common zero/nonzero pattern (uniform N-step strongly structural input and state observability) or at least for almost all system matrices that share a common zero/nonzero pattern (uniform N-step structural input and state observability). Based on some specific assumptions on the structure of the interactions between the unknown input and the network states, we show that such a characterization depends only on strongly structural (respectively, structural) observability properties of a suitable subsystem.