ON LAGRANGE STABILITY AND POISSON STABILITY OF THE DIFFERENTIAL-DYNAMIC SYSTEMS
Ключевые слова:
difference-dynamic system, continuity, Lyapunov functions, Lagrange stability, Poisson stability.Аннотация
The real difference-dynamic system is considered. The case of unlimited continuity of solutions is
investigated for this difference-dynamic system. Unlimited continuity to the right of solutions of the differencedynamic system is a necessary condition for Lyapunov stability of solutions of this system. Using functions similar
to Lyapunov functions, sufficient conditions for the unlimited continuity of solutions of the difference-dynamical
system are obtained. The concepts of Lagrange stability and Poisson stability are introduced. Relations between
Lyapunov functions and Lagrange stability are investigated. Using the discrete analogue of the second Lyapunov
method, the necessary and sufficient conditions for Lagrange stability of the solution of the difference-dynamical
system are obtained. A dynamic-difference system is considered for which a discrete operator is constructed, with the
help of which the Poisson stability of the system solutions is investigated.
