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
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/77340
Official URL:https://doi.org/10.1137/100790628
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