### Abstract

The authors examine necessary conditions for the existence of a universally observable system defined on a state space X. An attempt is made to prove that such a system is necessarily minimal and that, if X is smooth, then X is compact, connected with vanishing Euler characteristic. As a consequence of this and the classification, initiated by Poincare and Denjoy, of vector fields on the two-torus, it is shown that low-dimensional universally observable systems are unexpectedly rare.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Publisher | IEEE |

Pages | 963-965 |

Number of pages | 3 |

State | Published - 1987 |

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### ASJC Scopus subject areas

- Chemical Health and Safety
- Control and Systems Engineering
- Safety, Risk, Reliability and Quality

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(pp. 963-965). IEEE.

**ON THE TOPOLOGY AND GEOMETRY ASPECTS OF UNIVERSALLY OBSERVABLE SYSTEMS.** / Byrnes, C. I.; Dayawansa, W.; Martin, Carol.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE Conference on Decision and Control.*IEEE, pp. 963-965.

}

TY - GEN

T1 - ON THE TOPOLOGY AND GEOMETRY ASPECTS OF UNIVERSALLY OBSERVABLE SYSTEMS.

AU - Byrnes, C. I.

AU - Dayawansa, W.

AU - Martin, Carol

PY - 1987

Y1 - 1987

N2 - The authors examine necessary conditions for the existence of a universally observable system defined on a state space X. An attempt is made to prove that such a system is necessarily minimal and that, if X is smooth, then X is compact, connected with vanishing Euler characteristic. As a consequence of this and the classification, initiated by Poincare and Denjoy, of vector fields on the two-torus, it is shown that low-dimensional universally observable systems are unexpectedly rare.

AB - The authors examine necessary conditions for the existence of a universally observable system defined on a state space X. An attempt is made to prove that such a system is necessarily minimal and that, if X is smooth, then X is compact, connected with vanishing Euler characteristic. As a consequence of this and the classification, initiated by Poincare and Denjoy, of vector fields on the two-torus, it is shown that low-dimensional universally observable systems are unexpectedly rare.

UR - http://www.scopus.com/inward/record.url?scp=0023548235&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023548235&partnerID=8YFLogxK

M3 - Conference contribution

SP - 963

EP - 965

BT - Proceedings of the IEEE Conference on Decision and Control

PB - IEEE

ER -