Extending hysteresis operators to spaces of piecewise continuous functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:282

Article

Logemann, H ; Mawby, AD

关键词: causality;    hysteresis operators;    piecewise continuous functions;    piecewise monotone functions;    rate independence;    sampled-data systems;   

DOI  :  10.1016/S0022-247X(03)00097-0

来源: Elsevier

【 摘 要 】

We consider continuous-time hysteresis operators, defined 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 defined on the set 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 define 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. We apply the concepts and results described above in the context of sampled-data feedback control of linear systems with input hysteresis. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

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