Detail publikace

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

Originální název

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

Anglický název

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

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

BibTex


@article{BUT163757,
  author="Josef {Diblík} and Alexandra {Rodkina} and Zdeněk {Šmarda}",
  title="On local stability of stochastic delay nonlinear discrete systems with state-dependent noise.",
  annote="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.",
  chapter="163757",
  doi="10.1016/j.amc.2019.125019",
  howpublished="online",
  number="125019",
  volume="374",
  year="2020",
  month="january",
  pages="1--15",
  type="journal article in Web of Science"
}