The securable subspace of a linear stochastic system with malicious sensors and actuators

Analogous to the notions of controllable and unobservable subspaces, the recently introduced notions of securable and unsecurable subspaces for linear dynamical systems have important operational meaning in the context of secure control of deterministic linear dynamical systems. Specifically, given a multiple input, multiple output linear dynamical system, an arbitrary subset of whose sensors and actuators are malicious, the unsecurable subspace has the operational meaning as the set of states that the malicious actuators can steer the system to, without detection of the visit to such a state by the honest sensors in the system. In this paper, we examine these subspaces from the standpoint of a fully-observed stochastic linear dynamical system, and establish operational meanings for them in this context.

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