Journal ArticleDOI
A generalized canonical piecewise-linear representation
Claus Kahlert,Leon O. Chua +1 more
TLDR
An extension of the well-known canonical representation for continuous piecewise-linear functions is introduced in this article, which is capable of describing all piecewise linear functions in two dimensions, being no longer subject to any restrictions.Abstract:
An extension of the well-known canonical representation for continuous piecewise-linear functions is introduced. This form is capable of describing all piecewise-linear functions in two dimensions, being no longer subject to any restrictions. Moreover, it is shown that just one nesting of absolute-value functions is sufficient to cover the whole class. >read more
Citations
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BookDOI
Piecewise Linear Control Systems
Mikael Johansson,M. Johanssn +1 more
TL;DR: This thesis treats analysis and design of piecewise linear control systems, and it is shown how Lyapunov functions with a discontinuous dependence on the discrete state can be computed via convex optimization.
Linear complementarity systems
TL;DR: In this paper, the authors introduce a new class of dynamical systems called "linear complementarity systems" where the time evolution of these systems consists of a series of continuous phases separated by "events" which cause a change in dynamics and possibly a jump in the state vector.
Journal ArticleDOI
High-level canonical piecewise linear representation using a simplicial partition
TL;DR: A set of high-level canonical piecewiselinear (HL-CPWL) functions are proposed to form a representation basis for the set of piecewise linear functions f: D/spl rarr/R/sup 1/ defined over a simplicial partition of a rectangular compact set D in R/sup n/.
Journal ArticleDOI
Convex piecewise-linear fitting
Alessandro Magnani,Stephen Boyd +1 more
TL;DR: The method described, which is a variation on the K-means algorithm for clustering, seems to work well in practice, at least on data that can be fit well by a convex function.
Linear complementarity systems : a study in hybrid dynamics
TL;DR: In this article, a solution concept for linear complementarity systems is defined by combining a hybrid point-of-view and a distributional framework, and the solution trajectories are defined by a hybrid approach.
References
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Journal ArticleDOI
Section-wise piecewise-linear functions: Canonical representation, properties, and applications
Leon O. Chua,Sung-Mo Kang +1 more
TL;DR: In this article, a new closed form analytical formula for representing n-dimensional surfaces and scalar functions of n variables which are piecewise-linear over each cross section obtained by freezing any combination of n - 1 of the n coordinates is presented.
Journal ArticleDOI
Canonical piecewise-linear representation
Leon O. Chua,An-Chang Deng +1 more
TL;DR: In this paper, the necessary and sufficient conditions for the existence of a canonical piecewise-linear representation of one variable f:R/sup 1/ to R/sup n/ to n>1 have been proved.
Journal ArticleDOI
A global representation of multidimensional piecewise-linear functions with linear partitions
Sung-Mo Kang,Leon O. Chua +1 more
TL;DR: An analytical representation for m -dimensional piecewise-linear functions which are affine over convex polyhedral regions bounded by linear partitions is introduced in this paper, where explicit formulas are presented to compute the coefficients associated with this representation along with an example.
Journal ArticleDOI
Existence Theorems and a Solution Algorithm for Piecewise-Linear Resistor Networks
TL;DR: In this article, it was shown that an iterative algorithm (generalized Katzenelson algorithm) leads to a solution in a finite number of iteration steps, and the theory can be applied to most currently used nonlinear networks.
Related Papers (5)
Section-wise piecewise-linear functions: Canonical representation, properties, and applications
Leon O. Chua,Sung-Mo Kang +1 more
A global representation of multidimensional piecewise-linear functions with linear partitions
Sung-Mo Kang,Leon O. Chua +1 more