Mean square finite-time boundary stabilisation and H∞ boundary control for stochastic reaction-diffusion systems

Xiao-Zhen Liu, Kai-Ning Wu and Weihai Zhang

International Journal of Systems Science, 2019, vol. 50, issue 7, 1388-1398

Abstract: In this paper, the boundary control problem of stochastic reaction-diffusion systems (SRDSs) is studied. First, a distribution controller is designed, and a sufficient condition is established to achieve mean square finite-time stability. Then a boundary controller is proposed, and a criterion is obtained for mean square finite-time stability by using Poincaré's inequality and Gronwall's inequality. When the system is subject to external noise, a boundary $H_\infty $H∞ controller is presented for the systems with an $H_\infty $H∞ performance. Furthermore, a boundary controller is presented to ensure robust mean square finite-time stability of linear uncertain SRDSs. Numerical examples illustrate the validity of the theoretical results.

Date: 2019
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DOI: 10.1080/00207721.2019.1615574

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