### Abstract

The introductory chapter provides an overview of the Koopman operator framework. We present basic notion and definitions, including those related to the spectral properties of the operator. We also review numerical methods that are used to represent the operator on a finite-dimensional basis and to compute its spectral properties from data (DMD algorithm and Arnoldi-based methods). Finally, several extensions of the Koopman operator to input-ouput systems are reviewed.

Original language | English |
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Title of host publication | The Koopman Operator in Systems and Control |

Subtitle of host publication | Concepts, Methodologies, and Applications |

Editors | Alexandre Mauroy, Igor Mezic, Yoshihiko Susuki |

Publisher | Springer |

Chapter | 1 |

Pages | 3-33 |

Number of pages | 30 |

ISBN (Electronic) | 978-3-030-35713-9 |

ISBN (Print) | 978-3-030-35712-2 |

Publication status | Published - 2020 |

### Publication series

Name | Lecture Notes in Control and Information Sciences |
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Publisher | Springer |

Volume | 484 |

ISSN (Print) | 0170-8643 |

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## Cite this

Mauroy, A., Susuki, Y., & Mezić, I. (2020). Introduction to the Koopman operator in systems and control theory. In A. Mauroy, I. Mezic, & Y. Susuki (Eds.),

*The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications*(pp. 3-33). (Lecture Notes in Control and Information Sciences; Vol. 484). Springer.