The Cayley transform of the generator of a polynomially stable $C_0$-semigroup

Masashi Wakaiki

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arXiv · 2103.10553

The Cayley transform of the generator of a polynomially stable $C_0$-semigroup

Masashi Wakaiki

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Abstract

In this paper, we study the decay rate of the Cayley transform of the generator of a polynomially stable $C_0$-semigroup. To estimate the decay rate of the Cayley transform, for polynomial stability. Using this integral condition, we relate polynomial stability to Lyapunov equations. We also study robustness of polynomial stability for a certain class of structured perturbations.

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Masashi Wakaiki. 2021-03-18. The Cayley transform of the generator of a polynomially stable $C_0$-semigroup. https://arxiv.org/abs/2103.10553

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