# 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

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topLogemann, 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 -

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