On singular perturbations due to fast actuators in hybrid control systems

A stability result is given for hybrid control systems singularly perturbed by fast but continuous actuators. If a hybrid control system has a compact set globally asymptotically stable when the actuator dynamics are omitted, or equivalently, are infinitely fast, then the same compact set is semiglobally practically asymptotically stable in the finite speed of the actuator dynamics. This result, which generalizes classical results for differential equations, justifies using a simplified plant model that ignores fast but continuous actuator dynamics, even when using a hybrid feedback control algorithm.