ON FINITE CHARACTER GEOMETRICAL PROPERTY OF THE DIFFERENTIAL REALIZATION OF NONSTATIONARY HYPERBOLIC SYSTEMS

A. V. Lakeyev; V. A. Rusanov; A. V. Banshchikov; R. A. Daneev

A. V. Lakeyev Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia
V. A. Rusanov Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia
A. V. Banshchikov Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia
R. A. Daneev Department of Information Technologies of the East Siberian Institute of the MIA of Russia, Irkutsk, Russia

Article ID: 2433

Keywords: differential ealization; identification of hyperbolic model

Abstract

Topological-algebraic investigation of the problem of existence of realization of finite-dimensional continuous dynamic processes in the class of second-order ordinary differential equations in a separable Hilbert space has been conducted. Simultaneously, analytical-geometric conditions of continuity of the process of constructing projections for the Rayleigh-Ritz nonlinear functional operator together with computation of the fundamental group of its image have been determined. The results may be applied to a posteriori modeling nonstationary hyperbolic systems.

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