Publisher DOI: 10.48550/arXiv.2203.08469
arXiv ID: 2203.08469
Title: Observability for non-autonomous systems
Language: English
Authors: Bombach, Clemens 
Gabel, Fabian Nuraddin Alexander  
Seifert, Christian  
Tautenhahn, Martin 
Keywords: Functional Analysis; Analysis of PDEs; Optimization and Control; 35Q93, 47N70 (Primary) 93B07, 93B28 (Secondary)
Issue Date: 16-Mar-2022
Source: arXiv: 2203.08469 (2022)
Abstract (english): 
We study non-autonomous observation systems align* ẋ(t) = A(t) x(t), y(t) = C(t) x(t), x(0) = x₀∈ X, align* where (A(t)) is a strongly measurable family of closed operators on a Banach space X and (C(t)) is a family of bounded observation operators from X to a Banach space Y. Based on an abstract uncertainty principle and a dissipation estimate, we prove that the observation system satisfies a final-state observability estimate in Lʳ(E; Y) for measurable subsets E ⊆ [0,T], T > 0. An application of the above result to families of uniformly strongly elliptic differential operators A(t) on Lᵖ(ℝᵈ) and observation operators C(t)u = 𝟏Ω₍t₎ u is presented. In this setting, we give sufficient and necessary geometric conditions on the family of sets (Ω(t)) such that the corresponding observation system satisfies a final-state observability estimate.
Institute: Mathematik E-10 
Document Type: Preprint
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