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Systems with hysteresis in the feedback loop: existence,regularity and asymptotic behaviour of solutions

Published online by Cambridge University Press:  15 September 2003

Hartmut Logemann  and
Eugene P. Ryan
Hartmut Logemann
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, U.K.; hl@maths.bath.ac.uk. epr@maths.bath.ac.uk.
Eugene P. Ryan
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, U.K.; hl@maths.bath.ac.uk. epr@maths.bath.ac.uk.
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Abstract

An existence and regularity theorem is proved for integral equations of convolution type which contain hysteresis nonlinearities. On the basis of this result, frequency-domain stability criteria are derived for feedback systems with a linear infinite-dimensional system in the forward path and a hysteresis nonlinearity in the feedback path. These stability criteria are reminiscent of the classical circle criterion which applies to static sector-bounded nonlinearities. The class of hysteresis operators under consideration contains many standard hysteresis nonlinearities which are important in control engineering such as backlash (or play), plastic-elastic (or stop) and Prandtl operators. Whilst the main results are developed in the context of integral equations of convolution type, applications to well-posed state space systems are also considered.

Keywords

Absolute stabilityasymptotic behaviourfrequency-domain stability criteriahysteresis infinite-dimensional systemsintegral equationsregularity of solutions.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 9 , January 2003 , pp. 169 - 196
Copyright
© EDP Sciences, SMAI, 2003

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