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.

Type

journal article in Web of Science

Language

English

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.

Keywords

Nonlinear stochastic difference equations; Local stability; State dependent perturbations

Authors

DIBLÍK, J.; RODKINA, A.; ŠMARDA, Z.

Released

25. 1. 2020

Publisher

Elsevier

Location

PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND

ISBN

1873-5649

Periodical

Applied Mathematics and Computation

Year of study

374

Number

125019

State

United States of America

Pages from

1

Pages to

15

Pages count

15

URL

https://www-sciencedirect-com.ezproxy.lib.vutbr.cz/science/article/pii/S0096300319310112

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.",
  journal="Applied Mathematics and Computation",
  year="2020",
  volume="374",
  number="125019",
  pages="1--15",
  doi="10.1016/j.amc.2019.125019",
  issn="1873-5649",
  url="https://www-sciencedirect-com.ezproxy.lib.vutbr.cz/science/article/pii/S0096300319310112"
}