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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 equationsof convolution type which contain hysteresis nonlinearities. Onthe basis of this result, frequency-domain stability criteria arederived for feedback systems with a linear infinite-dimensionalsystem in the forward path and a hysteresis nonlinearity in thefeedback path. These stability criteria are reminiscent of theclassical circle criterion which applies to static sector-boundednonlinearities. The class of hysteresis operators underconsideration contains many standard hysteresis nonlinearitieswhich are important in control engineering such as backlash (orplay), plastic-elastic (or stop) and Prandtl operators. Whilst themain results are developed in the context of integral equations ofconvolution type, applications to well-posed state space systemsare also considered.

Keywords

Absolute stabilityasymptotic behaviourfrequency-domainstability criteriahysteresisinfinite-dimensional systemsintegralequationsregularity of solutions.

Information

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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