## Abstract

A low-gain integral controller with anti-windup component is presented for exponentially stable, linear, discrete-time, infinite-dimensional control systems subject to input nonlinearities and external disturbances. We derive a disturbance-to-state stability result which, in particular, guarantees that the tracking error converges to zero in the absence of disturbances. The discrete-time result is then used in the context of sampled-data low-gain integral control of stable well-posed linear infinite-dimensional systems with input nonlinearities. The sampled-date control scheme is applied to two examples (including sampled-data control of a heat equation on a square) which are discussed in some detail.

Original language | English |
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Pages (from-to) | 17-47 |

Number of pages | 31 |

Journal | Mathematical Control and Related Fields |

Volume | 12 |

Issue number | 1 |

DOIs | |

Publication status | Published - 31 Mar 2022 |

## Keywords

- Anti-windup methods
- Discrete-time
- Input-to-state stability
- Integral control
- Quantization
- Sampled-data control
- Saturation
- Well-posed infinite-dimensional systems

## ASJC Scopus subject areas

- Control and Optimization
- Applied Mathematics