MURPHYS-HSFS-2014 - 7th International Workshop on Multi-Rate Processes & Hysteresis, 2nd International Workshop on Hysteresis and Slow-Fast Systems, April 7-11, 2014 - Abstract
Klein, Olaf
In Brokate-Sprekels 1996, it is shown that every hysteresis operators acting on scalar-valued, continuous, piecewise monotone input functions can be represented by a functional acting on alternating strings. It is also shown that this representation formulae can be used to generated some hysteresis operators acting on scalar-valued, piecewise monotone input functions. In the current paper, a representation result is formulated for all hysteresis operators dealing with vector valued input functions being left-continuous, piecewise continuous, and piecewise monotaffine, i.e. being piecewise the composition of two functions such that the output of a monotone increasing function is used as input for an affine function. The operators are generated by functions acting on an admissible of set of strings of triples, with each triple consisting of a pairs of elements of the vector space combined with a boolean variable.