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AIMS Mathematics

2023, Volume 8, Issue 2: 4973-5006. doi: 10.3934/math.2023249
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Research article

Robust stability and passivity analysis for discrete-time neural networks with mixed time-varying delays via a new summation inequality

  • 1.
    Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 52290, Thailand
  • 2.
    Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
  • 3.
    Department of Mathematics, Thiruvalluvar University, Vellore 632115, Tamilnadu, India
  • 4.
    Rail System Institute of Rajamangala University of Technology Isan, Nakhon Ratchasima 30000, Thailand
  • Received: 02 September 2022 Revised: 24 November 2022 Accepted: 30 November 2022 Published: 12 December 2022

  • MSC : 37C75, 93C55, 92B20

  • The summation inequality is essential in creating delay-dependent criteria for discrete-time systems with time-varying delays and developing other delay-dependent standards. This paper uses our rebuilt summation inequality to investigate the robust stability analysis issue for discrete-time neural networks that incorporate interval time-varying leakage and discrete and distributed delays. It is a novelty of this study to consider a new inequality, which makes it less conservative than the well-known Jensen inequality, and use it in the context of discrete-time delay systems. Further stability and passivity criteria are obtained in terms of linear matrix inequalities (LMIs) using the Lyapunov-Krasovskii stability theory, coefficient matrix decomposition technique, mobilization of zero equation, mixed model transformation, and reciprocally convex combination. With the assistance of the LMI Control toolbox in Matlab, numerical examples are provided to demonstrate the validity and efficiency of the theoretical findings of this research.

    Citation: Jenjira Thipcha, Presarin Tangsiridamrong, Thongchai Botmart, Boonyachat Meesuptong, M. Syed Ali, Pantiwa Srisilp, Kanit Mukdasai. Robust stability and passivity analysis for discrete-time neural networks with mixed time-varying delays via a new summation inequality[J]. AIMS Mathematics, 2023, 8(2): 4973-5006. doi: 10.3934/math.2023249

    Related Papers:

  • The summation inequality is essential in creating delay-dependent criteria for discrete-time systems with time-varying delays and developing other delay-dependent standards. This paper uses our rebuilt summation inequality to investigate the robust stability analysis issue for discrete-time neural networks that incorporate interval time-varying leakage and discrete and distributed delays. It is a novelty of this study to consider a new inequality, which makes it less conservative than the well-known Jensen inequality, and use it in the context of discrete-time delay systems. Further stability and passivity criteria are obtained in terms of linear matrix inequalities (LMIs) using the Lyapunov-Krasovskii stability theory, coefficient matrix decomposition technique, mobilization of zero equation, mixed model transformation, and reciprocally convex combination. With the assistance of the LMI Control toolbox in Matlab, numerical examples are provided to demonstrate the validity and efficiency of the theoretical findings of this research.


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