| Extending Hysteresis Operators to Spaces of Piecewise Continuous Functions (2007) | |||||||||||||||
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| : We consider continuous-time hysteresis operators, dened to be causal and rate independent operators mapping input signals u : R+ ! R to output signals v : R+ ! R. We show how a hysteresis operator dened on the space of continuous piecewise monotone functions, can be naturally extended to piecewise continuous piecewise monotone functions. We prove that the extension is also a hysteresis operator and that a number of important properties of the original operator are inherited by the extension. Moreover, we dene the concept of a discrete-time hysteresis operator and we show that discretizing continuous-time hysteresis operators using standard sampling and hold operations leads to discrete-time hysteresis operators. Keywords: Causality, hysteresis operators, piecewise continuous functions, piecewise monotone functions, rate independence. AMS subject classications: 47H30, 47H99, 47J40, 93C57. This work was supported by the UK EPSRC Council (Grant GR/L78086). 1 Introduction Gen... | |||||||||||||||
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