Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Frequency Domain Conditions for the Existence of Finite-dimensional Projectors and Determining Observations of Attractors

Author(s):

Sergei Albertovich Popov

Saint-Petersburg State University

serg.pobeda@gmail.com

Volker Reitmann

70 corp.3, Botanicheskaya st,
Peterhof, Saint-Petersburg,
198516, Russia
Saint-Petersburg State University
professor of the Department of Applied Cybernetics
Prof. Dr.

vreitmann@aol.com

Abstract:

Frequency domain conditions for the existence of finite-dimensional projectors and determining observations for attractors of semi-dynamical systems in Hilbert spaces are derived. Evolutionary variational equations are considered as control systems in a rigged Hilbert space structure. As an example we investigate a coupled system of Maxwell's equations and the heat equation in one-space dimension. We show the controllability of the linear part and the frequency domain conditions for this example.

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