International audienceIn this paper we present a new method to perform the higher order sliding modes analysis of trajectories of hybrid systems with chattering behavior. This method improves our previous work [AC15] as it modifies numerical simulation algorithms to make them compute the higher order terms of the normal unit vectors of the systems dynamics whenever the first order sliding mode theory cannot be applied. Such modification does not affect the generality of our previous contribution in [AC15]. Our algorithm is general enough to handle both chattering on a single (n−1) switching manifold (i.e. chattering between two dynamics) as well as chattering on the intersection of finitely many intersected (n−1) switching manifolds. In this last case, we show by a special hierarchical application of convex combinations, that unique solutions can be found in general cases when the switching function takes the form of finitely many intersecting manifolds so that an efficient numerical treatment of the sliding motion constrained on the entire discontinuity region (including the switching intersection) is guaranteed. Illustrations of the techniques developed in this article are given on representative examples
