On the Relation between stability of continuous- and discrete-time evolution equations via the Cayley transform

Guo, B.Z. and Zwart, H.J. (2006) On the Relation between stability of continuous- and discrete-time evolution equations via the Cayley transform. Integral Equations and Operator Theory, 54 . pp. 349-383. ISSN 0378-620X

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Abstract:	n this paper we investigate and compare the properties of the semigroup generated by $A$ , and the sequence $A_d^n$ , $n \in {\mathbb N}$ , where $A_d= (I+A)(I-A)^{-1}$ . We show that if $A$ and $A^{-1}$ generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then $A_d$ is power bounded. For analytic semigroups we can prove stronger results. If $A$ is the infinitesimal generator of an analytic semigroup, then power boundedness of $A_d$ is equivalent to the uniform boundedness of the semigroup generated by $A$ .
Item Type:	Article
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/62874
Official URL:	http://dx.doi.org/10.1007/s00020-003-1350-9
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Metis ID: 238015