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CONTROLLABILITY AND OBSERVABILITY FOR NON-AUTONOMOUS EVOLUTION EQUATIONS: THE AVERAGED HAUTUS TEST

Abstract : We consider the observability problem for non-autonomous evolution systems (i.e., the operators governing the system depend on time). We introduce an averaged Hautus condition and prove that for skew-adjoint operators it characterizes exact observability. Next, we extend this to more general class of operators under a growth condition on the associated evolution family. We give an application to the Schrödinger equation with time dependent potential and the damped wave equation with a time dependent damping coefficient.
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https://hal.archives-ouvertes.fr/hal-01717316
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Submitted on : Monday, August 26, 2019 - 4:18:24 PM
Last modification on : Saturday, December 4, 2021 - 3:43:44 AM
Long-term archiving on: : Friday, January 10, 2020 - 4:31:25 PM

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  • HAL Id : hal-01717316, version 2

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El-Maati Ouhabaz, Bernhard Haak, Duc-Trung Hoang. CONTROLLABILITY AND OBSERVABILITY FOR NON-AUTONOMOUS EVOLUTION EQUATIONS: THE AVERAGED HAUTUS TEST. Systems & Control Letters, 2019, 133. ⟨hal-01717316v2⟩

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