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Input-to-state Stabilization of Delayed Semi-Markovian Jump Neural Networks Via Sampled-Data Control

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Abstract

This paper discusses the sampled-data input-to-state stabilization for delayed semi-Markovian jump neural networks subject to external disturbance. First, a hybrid closed-loop system is formulated, which contains continuous-time state signal, disturbance input signal, discrete-time control signal, and jumping parameters of the semi-Markovian process. Then, two time-dependent and mode-dependent Lyapunov functionals are constructed corresponding to different assumptions about the activation functions. Subsequently, two sufficient conditions concerning the sampled-data controller design are derived to ensure the mean-square input-to-state stability for the hybrid closed-loop system by utilizing the proposed Lyapunov functionals, a few inequalities, as well as some stochastic analysis techniques. It is worth remarking that the present conditions are capable of ensuring mean-square exponential stability of the closed-loop system in the absence of external disturbances. Lastly, a numerical example is employed to verify the validity of the proposed input-to-state stabilization methods.

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Acknowledgements

This work was supported by the Natural Science Foundation of the Anhui Higher Education Institutions (Nos. KJ2020A0248 and KJ2021ZD0129).

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Authors and Affiliations

  1. School of Computer Science & Technology, Anhui University of Technology, Ma’anshan, 243032, China

    Ling He, Wenhuang Wu & Jianping Zhou

  2. School of Computer and Information Engineering, Chuzhou University, Chuzhou, 239000, China

    Guangshun Yao

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  1. Ling He
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  2. Wenhuang Wu
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  3. Guangshun Yao
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He, L., Wu, W., Yao, G. et al. Input-to-state Stabilization of Delayed Semi-Markovian Jump Neural Networks Via Sampled-Data Control. Neural Process Lett 55, 3245–3266 (2023). https://doi.org/10.1007/s11063-022-11008-z

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