On the Hautus Test for Exponentially Stable $C_0$-Groups

DOI10.1137/080724733zbMath1193.47044OpenAlexW2017069511MaRDI QIDQ3566963

Birgit Jacob, Hans J. Zwart

Publication date: 10 June 2010

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/080724733

zbMATH Keywords

infinite-dimensional systems\(C_0\) semigroupsexact observabilityHautus testunbounded observation operatorapproximate observabilityinfinite-time admissibility

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Observability (93B07) Operator-theoretic methods (93B28) Control/observation systems in abstract spaces (93C25)

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Exact observability conditions for Hilbert space dynamical systems connected with Riesz basis of divided differences ⋮ Local indirect stabilization of same coupled evolution systems through resolvent estimates ⋮ Resolvent conditions for the control of parabolic equations ⋮ Characterization by observability inequalities of controllability and stabilization properties ⋮ Simplified conditions of initial observability for infinite-dimensional second-order damped dynamical systems ⋮ Exact observability, square functions and spectral theory ⋮ Infinite-time exact observability of Volterra systems in Hilbert spaces ⋮ Controllability and observability for non-autonomous evolution equations: the averaged Hautus test ⋮ Infinite-Time Admissibility and Exact Observability of Volterra Systems

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