Chattering analysis in sliding mode systems with inertial sensors

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