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.
Mots-clés : absolute stability, asymptotic behaviour, frequency-domain stability criteria, hysteresis, infinite-dimensional systems, integral equations, regularity of solutions
@article{COCV_2003__9__169_0,
author = {Logemann, Hartmut and Ryan, Eugene P.},
title = {Systems with hysteresis in the feedback loop : existence, regularity and asymptotic behaviour of solutions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {169--196},
publisher = {EDP-Sciences},
volume = {9},
year = {2003},
doi = {10.1051/cocv:2003007},
mrnumber = {1957097},
zbl = {1076.45004},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv:2003007/}
}
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 PY - 2003 SP - 169 EP - 196 VL - 9 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2003007/ DO - 10.1051/cocv:2003007 LA - en ID - COCV_2003__9__169_0 ER -
%0 Journal Article %A Logemann, Hartmut %A Ryan, Eugene P. %T Systems with hysteresis in the feedback loop : existence, regularity and asymptotic behaviour of solutions %J ESAIM: Control, Optimisation and Calculus of Variations %D 2003 %P 169-196 %V 9 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2003007/ %R 10.1051/cocv:2003007 %G en %F COCV_2003__9__169_0
Logemann, Hartmut; Ryan, Eugene P. Systems with hysteresis in the feedback loop : existence, regularity and asymptotic behaviour of solutions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 169-196. doi : 10.1051/cocv:2003007. http://archive.numdam.org/articles/10.1051/cocv:2003007/
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