Results on robust stabilization of asymptotically controllable systems by hybrid feedback

We show that a nonlinear system that is asymptotically controllable to a compact set can be stabilized by a hybrid feedback that is robust to small measurement noise, actuator error, and external disturbances. The construction of such a feedback hinges upon recasting a stabilizing patchy feedback in the hybrid framework. Auxiliary results on generic robustness of stability in hybrid systems are given.