### 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 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.

Original language | English (US) |
---|---|

Pages (from-to) | 458-483 |

Number of pages | 26 |

Journal | ESAIM - Control, Optimisation and Calculus of Variations |

Volume | 13 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Control and Optimization
- Computational Mathematics

### Cite this

*ESAIM - Control, Optimisation and Calculus of Variations*,

*13*(3), 458-483. https://doi.org/10.1051/cocv:2007022

}

*ESAIM - Control, Optimisation and Calculus of Variations*, vol. 13, no. 3, pp. 458-483. https://doi.org/10.1051/cocv:2007022

**Integral control of infinite-dimensional systems in the presence of hysteresis : An input-output approach.** / Logemann, Hartmut; Ryan, Eugene P.; Shvartsman, Ilya.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Integral control of infinite-dimensional systems in the presence of hysteresis

T2 - An input-output approach

AU - Logemann, Hartmut

AU - Ryan, Eugene P.

AU - Shvartsman, Ilya

PY - 2007/7/1

Y1 - 2007/7/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=34648817140&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34648817140&partnerID=8YFLogxK

U2 - 10.1051/cocv:2007022

DO - 10.1051/cocv:2007022

M3 - Article

AN - SCOPUS:34648817140

VL - 13

SP - 458

EP - 483

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

SN - 1292-8119

IS - 3

ER -