On the number of solutions of piecewise-linear resistive circuits

Hasler, M.; Schnetzler, Christoph

doi:10.1109/31.17586

Cited by 22 publications

(1 citation statement)

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“…Piecewise-linear models are widely used in diverse fields, such as circuit theory, image processing, system identification, economics and financial analysis, etc (Chua and Ying 1983; Chua and Deng 1985; Hasler and Schnetzler 1989; Yamamura and Ochiai 1992; Russo 2006; Feo and Storace 2004, 2007; Brooks 2008). The factor that prevalently motivates the use of this type of models is the simplicity of their structure which let them be efficiently implemented in both algorithms and hardware.…”

Section: Introductionmentioning

confidence: 99%

Transforming the canonical piecewise-linear model into a smooth-piecewise representation

et al. 2016

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A smoothed representation (based on natural exponential and logarithmic functions) for the canonical piecewise-linear model, is presented. The result is a completely differentiable formulation that exhibits interesting properties, like preserving the parameters of the original piecewise-linear model in such a way that they can be directly inherited to the smooth model in order to determine their parameters, the capability of controlling not only the smoothness grade, but also the approximation accuracy at specific breakpoint locations, a lower or equal overshooting for high order derivatives in comparison with other approaches, and the additional advantage of being expressed in a reduced mathematical form with only two types of inverse functions (logarithmic and exponential). By numerical simulation examples, this proposal is verified and well-illustrated.

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