This paper is concerned with integral control of systems with hysteresis. Using an input-output approach, it is shown that application of integral control to the series interconnection of either (a) a hysteretic input nonlinearity, an ${L}^{2}$-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity, or (b) an ${L}^{2}$-stable, time-invariant linear system and a hysteretic output nonlinearity, guarantees, under certain assumptions, tracking of constant reference signals, provided the positive integrator gain is smaller than a certain constant determined by a positivity condition in the frequency domain. The input-output results are applied in a general state-space setting wherein the linear component of the interconnection is a well-posed infinite-dimensional system.

Keywords: actuator nonlinearities, hysteresis, infinite-dimensional systems, input-output analysis, integral control, sensor nonlinearities

@article{COCV_2007__13_3_458_0, author = {Logemann, Hartmut and Ryan, Eugene P. and Shvartsman, Ilya}, title = {Integral control of infinite-dimensional systems in the presence of hysteresis : an input-output approach}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {458--483}, publisher = {EDP-Sciences}, volume = {13}, number = {3}, year = {2007}, doi = {10.1051/cocv:2007022}, mrnumber = {2329171}, zbl = {1123.93059}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2007022/} }

TY - JOUR AU - Logemann, Hartmut AU - Ryan, Eugene P. AU - Shvartsman, Ilya TI - Integral control of infinite-dimensional systems in the presence of hysteresis : an input-output approach JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2007 SP - 458 EP - 483 VL - 13 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007022/ DO - 10.1051/cocv:2007022 LA - en ID - COCV_2007__13_3_458_0 ER -

%0 Journal Article %A Logemann, Hartmut %A Ryan, Eugene P. %A Shvartsman, Ilya %T Integral control of infinite-dimensional systems in the presence of hysteresis : an input-output approach %J ESAIM: Control, Optimisation and Calculus of Variations %D 2007 %P 458-483 %V 13 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2007022/ %R 10.1051/cocv:2007022 %G en %F COCV_2007__13_3_458_0

Logemann, Hartmut; Ryan, Eugene P.; Shvartsman, Ilya. Integral control of infinite-dimensional systems in the presence of hysteresis : an input-output approach. ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 3, pp. 458-483. doi : 10.1051/cocv:2007022. http://www.numdam.org/articles/10.1051/cocv:2007022/

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