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

Abstract

Summary: A new canonical representation for a rather general class of piecewise- affine maps has been developed. The given canonical representation extends the canonical representation proposed by Chua and Kang into PWA 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 piecewise-affine circuits.