Stability Analysis Via Averaging For Singularly Perturbed Nonlinear Systems With Delays

In this work we consider stability of singularly perturbed nonlinear systems affected by time-delays. In particular, we consider the case when trajectories of the boundary layer system of such a system converge to a compact set. By combining the averaging method and the Lyapunov-Razumikhin approach, we obtained sufficient conditions for semi-global and practical stability based on conditions of the corresponding boundary layer system and the averaging model of the reduced slow-subsystem.