The asymptotic attraction and stability of hybrid stochastic functional systems with pantograph delay

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Mao, Wei and Jiang, Yanan and Hu, Liangjian and Mao, Xuerong (2025) The asymptotic attraction and stability of hybrid stochastic functional systems with pantograph delay. Mathematical Control and Related Files. ISSN 2156-8499 (https://doi.org/10.3934/mcrf.2025066)

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Abstract

In this paper, we investigate a class of hybrid stochastic functional systems with unbounded pantograph delays. By establishing the LaSalle theorem, we locate the limit sets for such hybrid systems, and thereby obtain several criteria for the asymptotic attraction and stability with exponential decay rate. Moreover, with the aid of M-matrix theory, we also derived some conditions under which attraction and stability are guaranteed. These conditions indicate that the asymptotic attraction and stability are robust with respect to stochastic perturbations. Finally, an example is presented to illustrate our results.

ORCID iDs

Mao, Wei, Jiang, Yanan, Hu, Liangjian and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
CORE (COnnecting REpositories)