A canonical representation for piecewise-affine maps and its applications to circuit analysis

A canonical representation for a rather general class of piecewise-affine maps has been developed. This canonical representation extends the canonical representation proposed by L.O. Chua and S.M. Hang (Proc. IEEE, vol.65, no.6, p.915-29, 1977) into PWA (piecewise-affine) partitions, which arise frequently in driving-point, transfer characteristics, and state equations. Thus, a universal canonical representation that is capable of characterizing circuit equations, state equations, and driving-point and transfer characteristics of piecewise-affine circuits in a compact global analytic form has been obtained. The canonical forms developed seem to be promising tools for computational purposes as well as for analytical studies of PWA circuits.>