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On local stability of stochastic delay nonlinear discrete systems with state-dependent noise

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  • Diblík, J.
  • Rodkina, A.
  • Šmarda, Z.

Abstract

We examine the local stability of solutions of a delay stochastic nonlinear difference equation with deterministic and state-dependent Gaussian perturbations. We apply the degenerate Lyapunov–Krasovskii functional technique and construct a sequence of events, each term of which is defined by a bound on a normally distributed random variable. Local stability holds on the intersection of these events, which has probability at least 1−γ,γ ∈ (0, 1). This probability can be made arbitrarily high by choosing the initial value sufficiently small. We also present a generalization to systems where a condition for stability is expressed in terms of the diagonal part of the unperturbed system, and computer simulations which illustrate our results.

Suggested Citation

  • Diblík, J. & Rodkina, A. & Šmarda, Z., 2020. "On local stability of stochastic delay nonlinear discrete systems with state-dependent noise," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    • Handle: RePEc:eee:apmaco:v:374:y:2020:i:c:s0096300319310112
    DOI: 10.1016/j.amc.2019.125019
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