  Actuator malfunctions may have disastrous consequences for systems not
designed to mitigate them. We focus on the loss of control authority over
actuators, where some actuators are uncontrolled but remain fully capable. To
counteract the undesirable outputs of these malfunctioning actuators, we use
real-time measurements and redundant actuators. In this setting, a system that
can still reach its target is deemed resilient. To quantify the resilience of a
system, we compare the shortest time for the undamaged system to reach the
target with the worst-case shortest time for the malfunctioning system to reach
the same target, i.e., when the malfunction makes that time the longest.
Contrary to prior work on driftless linear systems, the absence of analytical
expression for time-optimal controls of general linear systems prevents an
exact calculation of quantitative resilience. Instead, relying on Lyapunov
theory we derive analytical bounds on the nominal and malfunctioning reach
times in order to bound quantitative resilience. We illustrate our work on a
temperature control system.
