Robustness of discontinuous feedback via sample and hold control

We demonstrate that discontinuous feedback, either derived from or possessing a Lyapunov-type framework, can achieve robust stabilization to an attractor 𝒜 by utilizing a sample and hold controller. Our results rely on one main theorem, which essentially states 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 catalogue several applications of this robustness; e.g., robustness to measurement noise, computational delays, or fast actuator dynamics.