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Journal Nonlinear World №7 for 2016 г.
Article in number:
Exponential stability for nonstationary linear approach of nonlinear systems with distributed parameters
Keywords: nonlinear evolutionary equation distributed system exponential stability infinite-dimen¬sional oscillator
Authors:
O.V. Druzhinina - Dr.Sc. (Phys.-Math.), Professor, Chief Research Scientist, FRC «Computer Science and Control» of RAS (Mocsow) E-mail: ovdruzh@mail.ru E.V. Lisovsky - Ph.D. (Phys.-Math.), Associate Professor, Kaluga Branch of the Bauman MSTU E-mail: levgenijv@gmail.com V.L Vorontsova - Ph.D. (Phys.-Math.), Associate Professor, N.I. Lobachevsky Institute of Mathematics and Mechanics of the Kazan Federal University E-mail: VLVorontsova@yandex.ru
Abstract:
The method of modeling of the distributed systems by means of abstract dynamic systems in infinite-dimensional phase space is de-veloped in the paper. The approach to research of stability of models with the distributed parameters is offered on the basis of this method and Lyapunov methods of stability analysis. The problem of exponential stability of equilibrium state on non-stationary linear approach is studied taking into account properties of unboundedness and dissipativity of the operator of linear approach. Application to research of properties of oscillator model with infinite number of degrees of freedom is considered. The obtained results can be used for solving of stability problems of programmed motion and for modeling of technical systems with distributed parameters taking into account requirements of stability.
Pages: 47-54
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