Chattering analysis in sliding mode systems with inertial sensors

Singularly-perturbed relay control systems with 2nd-order sliding modes (SP2SM) are considered for modeling sliding-mode control systems with inertial sensors. It is shown that the asymptotically stable slow-motions integral manifold (ASSMIM) of a smooth singularly-perturbed system, describing the motion of the original SP2SM in the 2nd-order sliding domain, is the ASSMIM of the original SP2SM. For sliding-mode control systems with inertial sensors, sufficient conditions for the exponentially decreasing amplitude of chattering and the unlimited growth of frequency are found. A formula for the asymptotic representation of "ideal" switching surface oscillations is suggested for sliding-mode systems with inertial sensors.