Stability Analysis for a Class of Time-Varying Hybrid Difference Systems with Perturbations

• Alexey Platonov ^[1]
  1. [1] Saint Petersburg State University

     Saint Petersburg State University

     Rusia

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 1, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • The paper investigates the problem of stability for one class of nonlinear non-stationary difference systems with switching and impulsive effects. The issue of preserving the asymptotic stability of the given equilibrium position under the influence of non-stationary perturbations is studied. A special feature of the work is that the non-stationary coefficients present in the system and in the perturbations can increase unboundedly or, on the contrary, tend to zero. For such class of non-stationarities, the results of most well-known works are inapplicable. It is shown that restrictions for the perturbations, guaranteeing the preservation of the asymptotic stability, depend generally on the constraints imposed on the switching/impulse law in the considered system. As an auxiliary result, estimates for solutions of the nominal and perturbed system are established. To obtain the desired results, the method of Lyapunov functions is used. The difference systems considered in the paper can be constructed by applying the Eulerian computational scheme to the corresponding differential systems. Numerical examples illustrating the application of the obtained results are presented.

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