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

TL;DR

This paper investigates the decay properties of the Cayley transform of generators of polynomially stable $C_0$-semigroups, establishing links to Lyapunov equations and robustness under structured perturbations.

Contribution

It introduces new decay estimates for the Cayley transform in polynomial stability and explores robustness of this stability under structured perturbations.

Findings

Decay rate estimates for Cayley transform

Relation between polynomial stability and Lyapunov equations

Robustness results for structured perturbations

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.