Abstract
We will show first that the asymptotic stability of an infinite dimensional linear system does not imply its exponential stability and is not determined by the spectrum of the generator. Then we will prove that stable systems are characterized by their corresponding Liapunov equations. It is also proved that null controllability implies stabilizability and that under additional conditions a converse implication takes place.
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© 2008 Birkhäuser Boston
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Zabczyk, J. (2008). Stability and stabilizability. In: Mathematical Control Theory. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4733-9_15
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DOI: https://doi.org/10.1007/978-0-8176-4733-9_15
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4732-2
Online ISBN: 978-0-8176-4733-9
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