Title :
Canonical piecewise-linear representation
Author :
Chua, Leon O. ; Deng, An-Chang
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA, USA
fDate :
1/1/1988 12:00:00 AM
Abstract :
Every continuous piecewise-linear function of one variable f :R1→R1 has a unique canonical piecewise-linear representation. However, only a subclass of higher-dimensional piecewise-linear functions f:Rn→Rn, n>1, has a canonical piecewise-linear representation. It is proved that the necessary and sufficient conditions for the existence of a canonical piecewise-linear representation is that fpossess a consistent variation property. The geometrical constraints imposed by this property are analyzed and discussed in detail along with many examples
Keywords :
nonlinear network analysis; piecewise-linear techniques; canonical piecewise-linear representation; consistent variation property; continuous piecewise-linear function; geometrical constraints; network analysis; nonlinear circuits; Circuit analysis; Helium; Lattices; MOSFETs; Nonlinear circuits; Nonlinear equations; Partitioning algorithms; Performance analysis; Piecewise linear techniques; Sufficient conditions;
Journal_Title :
Circuits and Systems, IEEE Transactions on
