  We address the problem of state estimation, attack isolation, and control for
discrete-time Linear Time Invariant (LTI) systems under (potentially unbounded)
actuator false data injection attacks. Using a bank of Unknown Input Observers
(UIOs), each observer leading to an exponentially stable estimation error in
the attack-free case, we propose an estimator that provides exponential
estimates of the system state and the attack signals when a sufficiently small
number of actuators are attacked. We use these estimates to control the system
and isolate actuator attacks. Simulations results are presented to illustrate
the performance of the results.
