The singularly perturbed relay control systems (SPRCS) as mathematical mode
ls of chattering in the small neighborhood of the switching surface in slid
ing mode systems are examined. Sufficient conditions for existence and stab
ility of fast periodic solutions to the SPRCS are found. It is shown that t
he slow motions in such SPRCS are approximately described by equations deri
ved from equations for the slow variables of SPRCS by averaging along fast
periodic motions. It is shown that in the general case, when the equations
of a plant contain relay control nonlinearly, the averaged equations do not
coincide with the equivalent control equations or with the Filippov's defi
nition for the sliding motions in the reduced system; however, in the linea
r case, they coincide.