Stability analysis in continuous and discrete time, using the Cayley transform

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Besseling, Niels and Zwart, Hans (2010) Stability analysis in continuous and discrete time, using the Cayley transform. Integral Equations and Operator Theory, 68 (4). pp. 487-502. ISSN 0378-620X

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Abstract:For semigroups and for bounded operators we introduce the new notion of Bergman distance. Systems with a finite Bergman distance share the same stability properties, and the Bergman distance is preserved under the Cayley transform. This way, we get stability results in continuous and discrete time. As an example, we show that bounded perturbations lead to pairs of semigroups with finite Bergman distance. This is extended to a class of Desch–Schappacher perturbations.
Item Type:Article
Additional information:Open Access
Copyright:© 2010 The Author(s)
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/75125
Official URL:http://dx.doi.org/10.1007/s00020-010-1805-8
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