On the robustness to measurement noise and unmodeled dynamics of stability in hybrid systems

Results on robustness to measurement noise and unmodeled dynamics of stability in hybrid systems are presented. We show that arbitrarily small measurement noise can lead to lack of existence of solutions in hybrid systems. One solution to this problem is to pass the measurements through a filter. Robustness to measurement noise using this filtering is shown explicitly. We also study the effect of unmodeled sensor/actuator dynamics in the closed loop and we demonstrate that stability is robust to a class of singular perturbations. The results are illustrated for the inverted pendulum on a cart system when attempting to globally asymptotically stabilize the inverted position of the pendulum and the neutral cart position