A unified criterion for semiglobal and global finite/fixed-time stability of stochastic systems

Lin Fu, Shiguo Peng, Quanxin Zhu and Jiawei Zhuang

International Journal of Systems Science, 2025, vol. 56, issue 15, 3587-3602

Abstract: In this paper, semiglobal and global finite/fixed-time stability of a class of semilinear stochastic systems in Hilbert spaces are studied. By employing the stopping time technique and applying the infinite-dimensional Itô formula, a unified Lyapunov criterion is established under which global finite-time, global fixed-time, semiglobal finite-time and semiglobal fixed-time stability can all be obtained. This fills the research gaps in the finite/fixed-time stability of stochastic distributed parameter systems and the semiglobal finite/fixed-time stability of stochastic systems. Moreover, compared to existing results on finite/fixed-time stability for stochastic systems, our Lyapunov criterion can still work well under more stringent conditions. This is done by adding a term which can reflect the stabilising effect of the diffusion term and replacing original fractional power functions with a class of piecewise continuous fractional power functions that are no longer required to be increasing. Finally, illustrative examples are given and the obtained theoretical results are verified by numerical simulations.

Date: 2025
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DOI: 10.1080/00207721.2025.2471570

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