# Spectral conditions implied by observability

El Alaoui, Fatima-Zahrae
and
Zwart, Hans
and
Boutoulout, Ali
(2011)
*Spectral conditions implied by observability.*
SIAM Journal on Control and Optimization, 49
(2).
pp. 672-685.
ISSN 0363-0129

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Abstract: | It is well known that a finite-dimensional output space implies limitations on the systems properties, like observability and detectability. In this paper we extend this result for infinite-dimensional output spaces, under the condition that the output operator is relatively compact. We show that if this holds, and the system is exactly observable in finite-time, then the inverse of the infinitesimal generator must be compact. By means of an example we show that this result does not hold for exact observability in infinite-time. Using the Hautus test, we obtain spectral properties of the generator for this case. A consequence of this result is that if the system is exponentially detectable, then the unstable part of the spectrum consists of only point spectrum with finite multiplicity. |

Item Type: | Article |

Copyright: | © 2011 SIAM |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/77340 |

Official URL: | http://dx.doi.org/10.1137/100790628 |

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