Boundary control for stochastic reaction–diffusion systems with time-varying delays and Lévy noise

K. Mathiyalagan, N. Soundarya Lakshmi and Mohana Sundaram Muthuvalu

Chaos, Solitons & Fractals, 2026, vol. 209, issue P1

Abstract: This paper investigates the stabilization results for stochastic reaction–diffusion systems (SRDSs) with time-varying delays and Lévy noise. Based on the method of backstepping, an invertible Volterra integral transformation is chosen to convert the considered system to the target system. The explicit solution for the kernel function is found by the method of successive approximation and it is used for designing the boundary feedback controller. By constructing appropriate Lyapunov–Krasovskii functionals, sufficient conditions are derived for ensuring the stability of the target system. As the chosen transformation is invertible, the stability of the target system results in the stability of the considered system with control. Finally, the proposed results are verified using numerical examples.

Keywords: Reaction–diffusion; Stochastic systems; Backstepping; Lévy noise; Stability (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:209:y:2026:i:p1:s096007792600634x

DOI: 10.1016/j.chaos.2026.118493

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