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Generalized delay-dependent reciprocally convex inequality on stability for neural networks with time-varying delay

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  • Arunagirinathan, S.
  • Lee, T.H.

Abstract

This work presents a generalized delay-dependent reciprocally convex inequality (GDDRCI) to analyze the stability problem of neural networks (NNs) with time-varying delay. The proposed GDDRCI with its order m in this research improves the estimation accuracy of a reciprocal convex term and encompasses some existing reciprocally convex inequalities as a special case. Consequently, a novel Lyapunov–Krasovskii functional (LKF), which includes a delay-product type m-dependent term and utilizes the correlated cross-information about the states and nonlinear activation function, is formulated. Since the constructed GDDRCI and LKF, the conservatism of the resulting stability conditions of NNs is further decreased. Finally, four numerical examples are presented to demonstrate the importance of the theoretical results.

Suggested Citation

  • Arunagirinathan, S. & Lee, T.H., 2024. "Generalized delay-dependent reciprocally convex inequality on stability for neural networks with time-varying delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 109-120.
    • Handle: RePEc:eee:matcom:v:217:y:2024:i:c:p:109-120
    DOI: 10.1016/j.matcom.2023.10.013
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    1. Yang, Hanhua & Yan, Mengqing & Duan, Wenyong & Chen, Chong, 2024. "Low conservative stability criteria for discrete-time Lur’e systems with sector and slope constrained nonlinearities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 601-616.

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