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Stability conditions of linear time-varying dynamical systems

Keywords:

O.V. Druzhinina – Dr.Sc.(Phys.-Math.), Professor, Main Research Scientist, FRC «Computer Science and Control» of RAS (Moscow); Main Research Scientist, V.A. Trapeznikov Institute of Control Sciences of RAS (Moscow)
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


Qualitative properties of solutions of nonstationary linear systems of differential equations with continuous coefficients are studied. Stability conditions are obtained on the basis of the Lyapunov function method and the conditions of diagonal dominance. The properties of the logarithmic measure of the matrix of the right-hand side of the system are used for stability analysis.
Asymptotic stability conditions of certain classes of nonstationary linear dynamic systems are formulated. These conditions relate to the type of effective terms are quite comfortable to use. The prospect of further study is a qualitative study of nonstationary systems of more general form. The obtained stability conditions can be applied in technical systems control problems.

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