Input-and-state observability of structured network systems

Structured systems are linear systems whose state-space matrices have a fixed pattern of zeros, and their other entries are free parameters. Controllability and observability of these systems have been studied since the 80's, and recently this has become a hot topic in the study of networks. Structural results characterize properties true for almost all choices of the free parameters, and strongly structural results are true for all non-zero parameters.

All characterizations involve properties of some graphs associated with the zero pattern. Motivated by cyber-physical security, this talk presents analogous results on input-and-state observability, where both initial condition and an unknown input need to be reconstructed from the outputs.