Chattering on high gain control systems with fast actuator

The singularly perturbed systems with two small parameters are considered as a mathematical model of chattering in the sliding mode systems. The time constant of fast actuator is one of these parameters and the other corresponds to the high gain in saturated control law. The sufficient conditions and correlations between the small parameters due to which the amplitude of chattering is exponentially decreasing are found. The correction algorithms for slow motions approximate equations design, which allow one to take into account the influence of the actuators and high gain are proposed.