Publication detail

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

DIBLÍK, J. RODKINA, A. ŠMARDA, Z.

Original Title

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

English Title

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

Type

journal article in Web of Science

Language

en

Original 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.

English 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.

Keywords

Nonlinear stochastic difference equations; Local stability; State dependent perturbations

Released

25.01.2020

ISBN

1873-5649

Periodical

Applied Mathematics and Computation

Year of study

374

Number

125019

State

US

Pages from

1

Pages to

15

Pages count

15

URL

Documents

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"
}