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

Hartmut Logemann; Eugene P. Ryan

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 9, page 169-196
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Logemann, Hartmut, and Ryan, Eugene P.. "Systems with hysteresis in the feedback loop: existence, regularity and asymptotic behaviour of solutions." ESAIM: Control, Optimisation and Calculus of Variations 9 (2010): 169-196. <http://eudml.org/doc/90688>.

@article{Logemann2010,
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. },
author = {Logemann, Hartmut, Ryan, Eugene P.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Absolute stability; asymptotic behaviour; frequency-domain stability criteria; hysteresis infinite-dimensional systems; integral equations; regularity of solutions.; absolute stability; frequency-domain stability criteria; hysteresis; infinite-dimensional systems; integral equations; regularity of solutions},
language = {eng},
month = {3},
pages = {169-196},
publisher = {EDP Sciences},
title = {Systems with hysteresis in the feedback loop: existence, regularity and asymptotic behaviour of solutions},
url = {http://eudml.org/doc/90688},
volume = {9},
year = {2010},
}

TY - JOUR
AU - Logemann, Hartmut
AU - Ryan, Eugene P.
TI - Systems with hysteresis in the feedback loop: existence, regularity and asymptotic behaviour of solutions
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 9
SP - 169
EP - 196
AB - 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.
LA - eng
KW - Absolute stability; asymptotic behaviour; frequency-domain stability criteria; hysteresis infinite-dimensional systems; integral equations; regularity of solutions.; absolute stability; frequency-domain stability criteria; hysteresis; infinite-dimensional systems; integral equations; regularity of solutions
UR - http://eudml.org/doc/90688
ER -

References

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