Slow periodic motions in variable structure systems

Singularly perturbed relay control systems (SPRCS) with stable periodic motion in reduced systems are studied here. The slow motions integral manifold of such systems consists of parts that correspond to different values of control and the solutions of SPRCS contain the jumps from one part of the slow manifold to the other. The theorems about existence and stability of the slow periodic solutions are proved. An algorithm of asymptotic representation for this periodic solutions using a boundary layer method is suggested.