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Русская версия

**Sergei Albertovich Popov**

Saint-Petersburg State University

**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.

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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