Discretization of Second Lyapunov Method

• Autores: Eugene Polulyakh, Volodymyr Sharko, Igor Vlasenko
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 15, Nº 1, 2016, págs. 157-180
• Idioma: inglés
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• Resumen

  • We propose a new criterion of stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This approach includes a consideration of a family of hypersurfaces instead of the Lyapunov functions, and conditions on the right-hand part of the differential equation on them instead of conditions on a Lyapunov function along trajectories of the equation.