Further results on robustness of (Possibly discontinuous) sample and hold feedback

We demonstrate that sample and hold state feedback control (possibly discontinuous with respect to the state) is robust when the closed loop system possesses an appropriate Lyapunov function. We first show that if a Lyapunov decrease over sampling periods exists for the nominal system, this decrease can be maintained with some degradation relative to a sufficiently small additive perturbation. We then proceed to catalog several applications of this robustness, e.g., robustness to measurement noise, computational delays, or fast actuator dynamics.