Dynamics of singularly perturbed sliding flow in Filippov systems

The paper’s Theorem 1 asserts the O(ε) smallness bound for the displacement over times εt under Assumptions 1–3 in the repelling-sliding scenario S−<T−<T+<S+ (equation (9) in the paper), for trajectories that avoid repelling sliding . The candidate solution derives the same leading-order drift and uniform O(ε) remainder via a different argument (slow-manifold tracking and a balance identity for ḣ). One overclaim appears: the candidate states x(εt)−x(0)=εt frd,s(x0)+O(ε^2), whereas the paper only guarantees an O(ε) remainder and explains why time-dependent fluctuations may persist; the O(ε^2) improvement is not justified in general and can be dropped without affecting the main result .