## Abstract

We consider coupled systems consisting of an infinite-dimensional part and a finite-dimensional part connected in feedback, such as, for example, the well-known SCOLE system (a beam with a rigid body attached at one end). The external world interacts with the coupled system via the finite-dimensional part, which receives the external input and sends out the output. The infinite-dimensional part is assumed to be such that it becomes well-posed and strictly proper when connected in cascade with an integrator. Under several assumptions, we derive well-posedness and exact controllability results for such coupled systems. The first main result concerns the case when the input signal of the finite-dimensional part is the difference between the external input and the feedback signal. The second main result allows a more general structure for the finite-dimensional part. We also prove a result for the approximate controllability of coupled systems.

Original language | English |
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Pages (from-to) | 2719-2750 |

Number of pages | 32 |

Journal | SIAM Journal on Control and Optimization |

Volume | 48 |

Issue number | 4 |

DOIs | |

State | Published - 2009 |

## Keywords

- Admissible control operator
- Coupled system
- Exact controllability
- Simultaneous controllability
- Well-posed system