SLIDING MODES IN INTERSECTING SWITCHING SURFACES , I : BLENDING

When a flow, discontinuous across a switching surface, points ‘inward’ so one cannot leave, it induces a unique flow within the surface, called the sliding mode. When several such surfaces intersect, one would seek a flow within the intersection, but some difficulties arise. We explore here the extent of the ambiguity involved in this situation and then show that for a certain form of ‘natural mechanism for implementation’ (sigmoid blending) one does indeed inherit, as a residual effect of this implementation, sufficient information to characterize a well-defined sliding mode in the intersection of two switching surfaces.