Implicit descriptions of piecewise‐linear configurations
ISSN: 0332-1649
Article publication date: 1 December 2001
Abstract
By a polyhedral or piecewise‐linear configuration in Rn we mean the finite union of finite intersections of open or closed halfspaces. It is proved that every such configuration can be characterized by the single algebraic‐like equation involving only addition, subtraction, multiplication, absolute value and signum operators. Next, all such simplest implicit characterizations are found for idealized diodes, the ideal step function and the hysteresis function. Finally, the one‐dimensional infinite potential trough is analysed and the obtained equations are conjectured to be the simplest possible. All this allows among others to describe systems containing piecewise‐linear elements in a compact form suitable for further analytic studies.
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Citation
Cel, J. (2001), "Implicit descriptions of piecewise‐linear configurations", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 20 No. 4, pp. 923-936. https://doi.org/10.1108/EUM0000000005761
Publisher
:MCB UP Ltd
Copyright © 2001, MCB UP Limited