The observability radius of network systems

This paper introduces the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix, and dedicated sensors are positioned at a subset of nodes. We allow for perturbations of certain edge weights, with the objective of preventing observability of some modes of the network dynamics. Our work considers perturbations with a desired sparsity structure, thus extending the classic literature on the controllability and observability radius of linear systems. We propose an optimization framework to determine a perturbation with smallest Frobenius norm that renders a desired mode unobservable from a given set of sensor nodes. We derive optimality conditions and a heuristic optimization algorithm, which we validate through an example.