# Integral control of infinite-dimensional systems in the presence of hysteresis: an input-output approach

Hartmut Logemann; Eugene P. Ryan; Ilya Shvartsman

ESAIM: Control, Optimisation and Calculus of Variations (2007)

- Volume: 13, Issue: 3, page 458-483
- ISSN: 1292-8119

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topLogemann, Hartmut, Ryan, Eugene P., and Shvartsman, Ilya. "Integral control of infinite-dimensional systems in the presence of hysteresis: an input-output approach." ESAIM: Control, Optimisation and Calculus of Variations 13.3 (2007): 458-483. <http://eudml.org/doc/249991>.

@article{Logemann2007,

abstract = {
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 L2-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity, or (b) an L2-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.
},

author = {Logemann, Hartmut, Ryan, Eugene P., Shvartsman, Ilya},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Actuator nonlinearities; hysteresis; infinite-dimensional
systems; input-output analysis; integral control; sensor
nonlinearities; actuator nonlinearities; infinite-dimensional systems; sensor nonlinearities},

language = {eng},

month = {6},

number = {3},

pages = {458-483},

publisher = {EDP Sciences},

title = {Integral control of infinite-dimensional systems in the presence of hysteresis: an input-output approach},

url = {http://eudml.org/doc/249991},

volume = {13},

year = {2007},

}

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

DA - 2007/6//

PB - EDP Sciences

VL - 13

IS - 3

SP - 458

EP - 483

AB -
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 L2-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity, or (b) an L2-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.

LA - eng

KW - Actuator nonlinearities; hysteresis; infinite-dimensional
systems; input-output analysis; integral control; sensor
nonlinearities; actuator nonlinearities; infinite-dimensional systems; sensor nonlinearities

UR - http://eudml.org/doc/249991

ER -

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