Slow periodic motions with internal sliding modes in variable structure systems

Abstract

Singularly perturbed relay systems (SPRS) in which the reduced systems have the stable periodic motions with internal sliding modes are studied. The slow motion integral manifold of such systems consists of the parts which correspond to the di erent values of relay control and the solutions may contain the jumps from one part of the slow manifold to another. For such systems a theorem about existence and stability of the periodic solutions is proved. An algorithm of asymptotic representation for this periodic solutions using boundary layer method is presented. It is proved that in the neighbourhood of the break away point the asymptotic representation starts with the ®rst order boundary layer function.