Stability of Stochastic Reaction-Diffusion Systems via Boundary Sampled-Data Control

WANG Yunzhu

doi:10.21656/1000-0887.450309

Volume 47 Issue 4

Apr. 2026

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WANG Yunzhu. Stability of Stochastic Reaction-Diffusion Systems via Boundary Sampled-Data Control[J]. Applied Mathematics and Mechanics, 2026, 47(4): 468-486. doi: 10.21656/1000-0887.450309

Citation:

WANG Yunzhu. Stability of Stochastic Reaction-Diffusion Systems via Boundary Sampled-Data Control[J]. Applied Mathematics and Mechanics, 2026, 47(4): 468-486. doi: 10.21656/1000-0887.450309

Citation:

WANG Yunzhu. Stability of Stochastic Reaction-Diffusion Systems via Boundary Sampled-Data Control[J]. Applied Mathematics and Mechanics, 2026, 47(4): 468-486. doi: 10.21656/1000-0887.450309

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Stability of Stochastic Reaction-Diffusion Systems via Boundary Sampled-Data Control

doi: 10.21656/1000-0887.450309

WANG Yunzhu^,

Foundation Science Education Center, Hangzhou City University, Hangzhou 310015, P.R.China

Received Date: 2024-11-18
Rev Recd Date: 2025-12-15

Available Online: 2026-04-30

Abstract

Abstract

The stability of stochastic reaction-diffusion systems under boundary sampling control was discussed. With the fully accessible system state, a boundary sampled-data controller was proposed, and a piecewise discontinuous Lyapunov function related to the sampling interval was constructed. For stochastic reaction-diffusion systems, sufficient conditions for mean-square exponential stability, both in nominal and robust settings, were obtained with the Wirtinger inequality for spatial integrals and isomorphic discrete transformations, in the form of matrix inequalities. With the not fully accessible system state, an observer-based boundary sampled-data control strategy was proposed, and results for the mean-square exponential stability and the robust mean-square exponential stability of the system were obtained, respectively. Finally, the feasibility of the proposed methods was demonstrated through 3 numerical examples.
- boundary sampled-data control,
- stability,
- stochastic reaction-diffusion system,
- observer

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References(33)

References

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