This article is cited in 1 paper

Stochastic Systems

Partial stability in probability of nonlinear stochastic discrete-time systems with delay

V. I. Vorotnikov^a, Yu. G. Martyshenko<sup>b

a</sup> Peoples' Friendship University of Russia, Sochi branch
^b Gubkin Russian State University of Oil and Gas

Abstract: A system of nonlinear stochastic functional-difference equations with finite delay is considered. By assumption, this system has a “partial” trivial equilibrium (with respect to part of the state variables). The problem under study is to analyze partial stability in probability of this equilibrium: stability is considered with respect to part of the variables determining it. The problem is solved using a discrete-stochastic modification of the method of Lyapunov–Krasovskii functionals. Conditions for partial stability in probability are established. An example is provided to illustrate the features of the proposed approach and the rationale for introducing a one-parameter family of functionals.

Keywords: system of nonlinear stochastic functional-difference equations with finite delay, partial stability in probability, method of Lyapunov–Krasovskii functionals.

Presented by the member of Editorial Board: P. V. Pakshin

Received: 20.09.2023
Revised: 15.03.2024
Accepted: 30.05.2024

DOI: 10.31857/S0005231024080021

 English version: Automation and Remote Control, 2024, 85:8, 674–684