### 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) |
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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 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

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

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