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Journal Nonlinear World №3 for 2017 г.
Article in number:
Stability conditions of nonstationary systems of differential equations
Keywords: stability linear nonstationary system perturbed system Lyapunov\'s function coefficient conditions logarithmic norm of a matrix
Authors:
O.V. Druzhinina - Dr.Sc. (Phys.-Math.), Professor, Chief Research Scientist, FRC «Computer Science and Control» of RAS, 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
Abstract:
Qualitative properties of solutions of three-dimensional nonstationary systems of differential equations with allowance for constraints for the coefficients and perturbing functions are studied. The stability conditions on the basis of a method of Lyapunov functions and by means of properties of a logarithmic norm of a matrix and conditions of diagonal domination are obtained for the linear case. The stability conditions on the basis of properties of linear part and taking into account the restrictions superimposed on non-linear function of perturbation are offered for a nonlinear case. Based on the properties of diagonal dominance and properties of logarithmic matrix sufficient stability conditions relate to effective conditions that can be used for control problems and for stability analysis of dynamic models of natural sciences and engineering. Suggested stability conditions of solutions of nonlinear systems cover a wide class of perturbing functions and can be used while studying stability for models of perturbed systems.
Pages: 54-58
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