We demonstrate the stability of observability estimates for solutions to wave and Schrödinger equations subjected to additive perturbations. This work generalises recent averaged observability/control results by allowing for systems consisting of operators of different types. We also consider the simultaneous observability problem by which one tries to estimate the energy of each component of a system under consideration. Our analysis relies on microlocal defect tools, in particular on standard H-measures when the main system dynamic is governed by the wave operator, and parabolic H-measures in the case of the Schrödinger operator.

Accepted:

DOI: 10.1051/cocv/2016074

Keywords: Averaged control, robust observability, parabolic H-measures

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@article{COCV_2018__24_1_45_0, author = {Lazar, Martin}, title = {Stability of observations of partial differential equations under uncertain perturbations}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {45--61}, publisher = {EDP-Sciences}, volume = {24}, number = {1}, year = {2018}, doi = {10.1051/cocv/2016074}, mrnumber = {3764133}, zbl = {1396.93030}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2016074/} }

TY - JOUR AU - Lazar, Martin TI - Stability of observations of partial differential equations under uncertain perturbations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 45 EP - 61 VL - 24 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016074/ DO - 10.1051/cocv/2016074 LA - en ID - COCV_2018__24_1_45_0 ER -

%0 Journal Article %A Lazar, Martin %T Stability of observations of partial differential equations under uncertain perturbations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 45-61 %V 24 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016074/ %R 10.1051/cocv/2016074 %G en %F COCV_2018__24_1_45_0

Lazar, Martin. Stability of observations of partial differential equations under uncertain perturbations. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 1, pp. 45-61. doi : 10.1051/cocv/2016074. http://archive.numdam.org/articles/10.1051/cocv/2016074/

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