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Exponential Stability for Delayed Octonion-Valued Recurrent Neural Networks

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Abstract

Over the last few years, neural networks with values in multidimensional domains have gained a lot of interest. A non-associative normed division algebra which generalizes the complex and quaternion algebras is represented by the octonion algebra. It does not fall into the category of Clifford algebras, which are associative. Delayed octonion-valued recurrent neural networks are introduced, for which the states and weights are octonions. A sufficient criterion is given in the form of linear matrix inequalities, which assures the global exponential stability of the equilibrium point for the proposed networks. Lastly, a numerical example illustrates the correctness of the theoretical results.

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Author information

Authors and Affiliations

  1. Department of Computer and Software Engineering, Polytechnic University Timişoara, Blvd. V. Pârvan, No. 2, 300223, Timişoara, Romania

    Călin-Adrian Popa

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  1. Călin-Adrian Popa
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Correspondence to Călin-Adrian Popa .

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Editors and Affiliations

  1. Universidad de Granada , Granada, Spain

    Ignacio Rojas

  2. University of Malaga , Malaga, Spain

    Gonzalo Joya

  3. Polytechnic University of Catalonia, Vilanova i la Geltrú, Barcelona, Spain

    Andreu Catala

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Popa, CA. (2017). Exponential Stability for Delayed Octonion-Valued Recurrent Neural Networks. In: Rojas, I., Joya, G., Catala, A. (eds) Advances in Computational Intelligence. IWANN 2017. Lecture Notes in Computer Science(), vol 10305. Springer, Cham. https://doi.org/10.1007/978-3-319-59153-7_33

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  • DOI: https://doi.org/10.1007/978-3-319-59153-7_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59152-0

  • Online ISBN: 978-3-319-59153-7

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