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Novel fixed-time stability criteria of nonlinear systems and applications in fuzzy competitive neural network and Chua’s oscillator

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Abstract

Since the fixed-time stability forms of nonlinear systems satisfy strict conditions, there are few general forms for nonlinear systems to achieve fixed-time stability. This work proposes a new class of more general fixed-time stability criteria. It is worth mentioning that, compared with the traditional method of estimating the convergence time, this paper obtains a more conservative stable time estimation formula through the integration method of the generalized integral mean theorem. In addition, given that the fixed-time stabilization of neural networks and chaotic oscillators have attracted extensive attention in recent years, and there are still many fixed-time stabilizations of nonlinear systems that have not been studied. Therefore, a discontinuous controller is designed in this paper. The above stability theory results are applied to the fixed-time stabilization of the Takagi-Sugeno (T-S) fuzzy competitive neural network and chaotic system (coupled Chua’s oscillator). Finally, the validity and applicability of the theoretical results are verified by examples.

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Acknowledgements

The authors gratefully acknowledge anonymous referees’ comments and patient work. This work was supported in part by the National Natural Science Foundation of China under Grant 62236005, 61936004 and U1913602.

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Authors and Affiliations

  1. School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, 430074, China

    Fangmin Ren, ** Wang & Zhigang Zeng

  2. School of Artificial Intelligence and Automation and Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan, 430074, China

    Fangmin Ren, ** Wang & Zhigang Zeng

  3. Hubei Key Laboratory of Brain-inspired Intelligent Systems, Huazhong University of Science and Technology, Wuhan, 430074, China

    Fangmin Ren, ** Wang & Zhigang Zeng

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  1. Fangmin Ren
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  2. ** Wang
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  3. Zhigang Zeng
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Correspondence to ** Wang.

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Ren, F., Wang, X. & Zeng, Z. Novel fixed-time stability criteria of nonlinear systems and applications in fuzzy competitive neural network and Chua’s oscillator. Neural Comput & Applic 35, 16527–16542 (2023). https://doi.org/10.1007/s00521-023-08523-y

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  • DOI: https://doi.org/10.1007/s00521-023-08523-y

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