Generic detectability and isolability of topology failures in networked linear systems

This article studies the possibility of detecting and isolating topology failures (including link and node failures) of a networked system from subsystem measurements, in which subsystems are of fixed high-order linear dynamics, and the exact interaction weights among them are unknown. We prove that in such a class of networked systems with the same network topologies, the detectability and isolability of a given topology failure (set) are generic properties, indicating that it is the network topology that dominates the property of being detectable or isolable for a failure (set). We first give algebraic conditions for detectability, and isolability of arbitrary parameter perturbations for a lumped plant and then derive graph-theoretical necessary and sufficient conditions for generic detectability and isolability of topology failures for the networked systems. On the basis of these results, we consider the problems of deploying the smallest set of sensors for generic detectability and isolability. We reduce the associated sensor placement problems to the hitting set problems, which can be effectively solved by greedy algorithms with guaranteed approximation performances.