Discussing Semigroup Bounds with Resolvent Estimates

Helffer, Bernard; Sjöstrand, Johannes; Viola, Joe

doi:10.1007/s00020-024-02754-x

Integr. Equ. Oper. Theory

2024

DOI: 10.1007/s00020-024-02754-x

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Discussing Semigroup Bounds with Resolvent Estimates

Bernard Helffer,

Johannes Sjöstrand,

Joe Viola

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2024

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Cited by 2 publications

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Prescribing transport equation solution's decay via multiplicity manifold and autoregressive boundary control

Ammari,

Boussaada,

Niculescu

et al. 2024

Intl J Robust & Nonlinear

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This article addresses the boundary control problem of the transport equation. Namely, we propose a control method, which is merely a delayed output feedback relying on a partial pole placement idea, that consists in assigning an appropriate exponential decay rate to the closed‐loop system's solution. The proposed control structure appearing in the transport boundary, which has proven its effectiveness in controlling finite dimensional systems, consists of an autoregressive relation linking the transport equation's input and output. The obtained result provides an analytical lower bound for the solution's exponential decay. The contribution is concluded with a numeric discussion on the concrete implementation of the method with a special emphasis on the delay seen as a control parameter.

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Prescribing transport equation solution's decay via multiplicity manifold and autoregressive boundary control

Ammari,

Boussaada,

Niculescu

et al. 2024

Intl J Robust & Nonlinear

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show abstract

Stability estimates for semigroups in the Banach case

Helffer

2024

J. Evol. Equ.

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Discussing Semigroup Bounds with Resolvent Estimates

Cited by 2 publications

References 16 publications

Prescribing transport equation solution's decay via multiplicity manifold and autoregressive boundary control

Prescribing transport equation solution's decay via multiplicity manifold and autoregressive boundary control

Stability estimates for semigroups in the Banach case

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