Asymptotic Controllability and Robust Asymptotic Stabilizability

Abstract We study asymptotic controllable systems for which there exists no smooth stabilizing state feedback. We consider a class of hybrid feedback. We define a class of solutions which is a generalization of Caratheodory solutions and Euler solutions. We prove that, in terms of such solutions, the origin of all globally asymptotically controllable systems can be globally asymptotically stabilized via a hybrid patchy feedback with robustness to measurement noises, actuator errors and external disturbances.