Polyhedral Elements: a New Approach for Capturing All the Equilibrium Points of Piecewise-Linear Circuits

An entirely new algorithm to find all the equilibrium points of piecewise-linear (PWL) circuits is presented. To this aim, the new class of the so-called polyhedral circuits, associated to the PWL ones, are defined by replacing the PWL elements with the polyhedral elements. The algorithm is structured as a genealogical tree, whose nodes represent specific polyhedral circuits. All the equilibrium points of the original PWL circuit can be captured by the analysis of these nodes. This analysis requires the solution of the Phase I of Linear Programming (LP) problems, one problem for each node. An example shows the capabilities of this algorithm.