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Robust stability of stochastic uncertain recurrent neural networks with Markovian jumping parameters and time-varying delays

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Abstract

In this paper, stability of stochastic recurrent neural networks with Markovian jumping parameters and time-varying delays is considered. A novel linear matrix inequality (LMI)-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of Markovian jumping stochastic recurrent neural networks with norm bounded uncertainties and time-varying delays. To reflect the most dynamical behaviors of the system, both parameter uncertainties and stochastic disturbance are considered, where parameter uncertainties enter into all the system matrices, stochastic disturbances are given in the form of a Brownian motion. The stability conditions are derived using Lyapunov–Krasovskii approach, in combined with the LMI techniques. The delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay should be 1 is removed. Finally, numerical examples are given to demonstrate the correctness of the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Thiruvalluvar University, Vellore, Tamilnadu, 632 106, India

    M. Syed Ali

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Correspondence to M. Syed Ali.

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The work of the author was supported by National Board for Higher Mathenatics (NBHM) grant under sanction No. 2/48(10)/2011-R&D- II/865.

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Syed Ali, M. Robust stability of stochastic uncertain recurrent neural networks with Markovian jumping parameters and time-varying delays. Int. J. Mach. Learn. & Cyber. 5, 13–22 (2014). https://doi.org/10.1007/s13042-012-0124-6

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  • DOI: https://doi.org/10.1007/s13042-012-0124-6

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