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Robust \(\mathcal {H}_{\infty }\) control of uncertain time-delay Markovian jump quaternion-valued neural networks subject to partially known transition probabilities: direct quaternion method

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Abstract

This paper addresses the issue of robust stochastic stabilization and \(\mathcal {H}_{\infty }\) control of uncertain time-delay Markovian jump quaternion-valued neural networks (MJQVNNs) subject to partially known transition probabilities. First, the direct quaternion method is proposed to analyse the MJQVNNs, which is different from some conventional methods in that the former is without any decomposition for systems. After that, in order to estimate the upper bound of the derivative of the constructed Lyapunov–Krasovskii functional (LKF) more accurately, the real-valued convex inequality is extended to quaternion domain. Then, by designed the mode-dependent state feedback controllers, the robust stochastic stabilization conditions of MJQVNNs are given for the admissible uncertainties, and reduce the influence of input disturbance on the controlled output to a specified performance level. Lastly, two numerical examples are given to illustrate the effectiveness of the proposed method.

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The authors declare that the data supporting the findings of this study are available within the article.

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Acknowledgements

This work was supported by the National Nature Science Foundation under Grant 12061088; Fundamental Research Funds for the Central Universities under Grant GK201905001; Natural Science Basic Research Plan in Shaanxi Province of China (No. 2022JQ-034).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710119, China

    Jinlong Shu & Baowei Wu

  2. School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, 650500, China

    Lianglin Xiong

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  1. Jinlong Shu
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  2. Baowei Wu
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Correspondence to Baowei Wu or Lianglin Xiong.

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Shu, J., Wu, B. & Xiong, L. Robust \(\mathcal {H}_{\infty }\) control of uncertain time-delay Markovian jump quaternion-valued neural networks subject to partially known transition probabilities: direct quaternion method. Cogn Neurodyn 17, 767–787 (2023). https://doi.org/10.1007/s11571-022-09846-7

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  • DOI: https://doi.org/10.1007/s11571-022-09846-7

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