  In this paper, we address the issue of quantifying maximum actuator
degradation in linear time-invariant dynamical systems. We present a new
unified framework for computing the state-feedback controller gain that meets a
user-defined closed-loop performance criterion while also maximizing actuator
degradation. This degradation is modeled as a first-order filter with additive
noise. Our approach involves two novel convex optimization formulations that
concurrently determine the controller gain, maximize actuator degradation, and
maintain the desired closed-loop performance in both the $H_2$ and $H_{\infty}$
system norms. The results are limited to open-loop stable systems. We
demonstrate the application of our results through the design of a full-state
feedback controller for a model representing the longitudinal motion of the
F-16 aircraft.
