Actuation attacks on constrained linear systems: a set-theoretic analysis

This paper considers a constrained discrete-time linear system subject to actuation attacks. The attacks are modelled as false data injections to the system, such that the total input (control input plus injection) satisfies hard input constraints. We establish a sufficient condition under which it is not possible to maintain the states of the system within a compact state constraint set for all possible realizations of the actuation attack. The developed condition is a simple function of the spectral radius of the system, the relative sizes of the input and state constraint sets, and the proportion of the input constraint set allowed to the attacker.