Abstract
As the title indicates, we study the stability of strongly continuous semigroups. We distinguish between exponential, strong, and weak stability. We show that the stability cannot be concluded from the spectrum of the infinitesimal generator, i.e., the spectrum determined growth assumption does not need to hold. For our classes of systems; spatially invariant operators, Riesz-spectral operators, and delay equations, we show that this growth assumption does hold. Since Sylvester equations can be solved under proper stability assumptions, this topic is part of the chapter. The chapter ends with a set of 22 exercises and a notes and references section.
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Curtain, R., Zwart, H. (2020). Stability. In: Introduction to Infinite-Dimensional Systems Theory. Texts in Applied Mathematics, vol 71. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-0590-5_4
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DOI: https://doi.org/10.1007/978-1-0716-0590-5_4
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-0716-0588-2
Online ISBN: 978-1-0716-0590-5
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