### Abstract

A fundamental question in systems and control theory concerns the characterization of the set of achievable closed-loop systems for a given plant system and a controller system to be designed. This problem, for example, shows up in assessing the ’limits of performance’ of a controlled system. Similar problems have been studied by researchers in automata theory and discrete event systems replacing the notion of closed-loop system by the composition of a given system and its controller. In this paper this problem is addressed in a general behavioral context. Necessary and often sufficient conditions for a behavior to be achievable are given, and for any achievable behavior a canonical controller is defined. These results generalize previously obtained results obtained for finite-dimensional linear systems. Next these general results are applied to classes of automata and hybrid systems.

Original language | Undefined |
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Title of host publication | Proceedings of the 41st IEEE Conference on Decision and Control |

Place of Publication | Las Vegas, Nevada, U.S.A. |

Publisher | IEEE |

Pages | 7-12 |

Number of pages | 6 |

ISBN (Print) | 0-7803-7516-5 |

Publication status | Published - Dec 2002 |

Event | 41st IEEE Conference on Decision and Control, CDC 2002 - Las Vegas, United States Duration: 10 Dec 2002 → 13 Dec 2002 Conference number: 41 |

### Publication series

Name | |
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Publisher | IEEE |

Volume | 1 |

ISSN (Print) | 0191-2216 |

### Conference

Conference | 41st IEEE Conference on Decision and Control, CDC 2002 |
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Abbreviated title | CDC |

Country | United States |

City | Las Vegas |

Period | 10/12/02 → 13/12/02 |

### Keywords

- EWI-16743
- METIS-210906
- IR-69142

## Cite this

van der Schaft, A., & Anak Agung Julius, A. A. J. (2002). Achievable behavior by composition. In

*Proceedings of the 41st IEEE Conference on Decision and Control*(pp. 7-12). Las Vegas, Nevada, U.S.A.: IEEE.