  We study the stability properties of the interconnection of an LTI dynamical
plant and a controller that generates control signals that are maliciously
compromised by an attacker. We consider two classes of controllers: a static
output-feedback controller, and a dynamical gradient-flow controller that seeks
to steer the output of the plant towards the solution of a convex optimization
problem. We analyze the stability of the system under a class of switching
attacks that persistently modify the control inputs generated by the
controllers. The stability analysis leverages the framework of Hybrid Dynamical
Systems, Lyapunov-based arguments for switching systems with unstable modes,
and singular perturbation theory. Our results show that the stability of the
interconnected system can be preserved when an attack defense mechanism can
mitigate "sufficiently often" the activation time of the attack action in any
bounded time interval. We present simulation results that corroborate the
technical findings.
