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 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://www.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://www.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://www.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, Volume 9 (2003), pp. 169-196. doi : 10.1051/cocv:2003007. http://www.numdam.org/articles/10.1051/cocv:2003007/

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