Piecewise-linear theory and computation of solutions of homeomorphic resistive networks

Author

Chien, Ming-Jeh

Volume

24

Issue

3

fYear

1977

fDate

3/1/1977 12:00:00 AM

Firstpage

118

Lastpage

127

Abstract

Piecewise-linear resistive networks can be characterized by the equation $f(x)=J^{(m)}x + w^{(m)} = y, m = 0, l, \\cdots ,l,$ where $l$ is a finite positive number. The domain ( $n$ -dimensional Euclidean space) is divided into $l+1$ regions (closed convex polyhedrons). In each region $j(m)$ is a constant $n \\times n$ matrix and $w^{(m)}$ is a constant $n$ -vector. In this paper, we derive necessary and sufficient conditions for the function $f(x)$ to be a homeomorphism. Different formulations of network equations are investigated, and results in terms of the matrices $J^{(m)}$ \´s are obtained. An algorithm with a new perturbation method is also developed which is capable of locating the unique solution in a finite number of steps. The work is different from the early work by Kuh and Fujisawa in many ways; comparisons are presented.

Keywords

Nonlinear network analysis; Nonlinear networks; Resistive networks; Biographies; Computer networks; Differential equations; Home computing; Jacobian matrices; Perturbation methods; Piecewise linear techniques; Resistors; Sufficient conditions; Vectors;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/TCS.1977.1084315

Filename

1084315