Slow periodic motions in the singularly perturbed relay control systems

The singularly perturbed relay control systems (SPRCS) which have the stable periodic motions in the reduced systems are studied. The slow motions integral manifold of such systems consists of the parts which correspond to different values of relay control and the solutions contain the jumps from the the one part of slow manifold to the other. Three classes of such systems are considered: systems without sliding modes, systems which contain internal sliding modes and systems with time delay. For such systems the theorems about existence and stability of the slow periodic solutions are proved. The algorithm of asymptotic representation for this periodic solutions using boundary layer method is suggested.