Singularly Perturbed Analysis of Chattering in Relay Control Systems

For sliding-mode control systems with fast actuators, suffi- cient conditions for the exponential decreasing of the amplitude of chat- tering and unlimited growth of frequency are found. The connection be- tween the stability of actuators and the stability of the plant on the one hand and the stability of the sliding-mode system as the whole on the other hand is investigated. The algorithm for correction of sliding-mode equa- tions is suggested for taking into account the presence of fast actuators.