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:	Mathematical Systems and Control Theory (MSCT)
Link to this item:	http://purl.utwente.nl/publications/77340
Official URL:	http://dx.doi.org/10.1137/100790628
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