Finding All Solutions of Piecewise-Linear Resistive Circuits Using Triangular LP Test

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits. This algorithm is based on a simple test (called the LP test) for nonexistence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is formulated as a linear programming problem by surrounding component PWL functions by rectangles. In this paper, an LP test algorithm using both rectangles and triangles is proposed. It is shown that the LP test becomes more powerful and more efficient by introducing the idea of coordinate transformation to the oblique coordinate system and by using the dual simplex method throughout the algorithm.