Sliding Modes in Intersecting Switching Surfaces, Ii: Hysteresis

When a ow, discontinuous across a switching surface, points \inward" so one cannot leave, it induces a unique ow within the surface, called the sliding mode. Uniqueness of sliding modes does not obtain in general when several such surfaces intersect, and models must be reened. Following our earlier papers, we investigate the consequences of such reene-ments. We show that a natural mechanism, to wit hysteresis, which has been extensively investigated for one switching surface, generically leads to a well-deened sliding mode in the intersection of two switching surfaces.