Practical exponential stability with respect to $ h- $manifolds of discontinuous delayed Cohen–Grossberg neural networks with variable impulsive perturbations

Gani Stamov; Ekaterina Gospodinova; Ivanka Stamova; Gani Stamov; Ekaterina Gospodinova; Ivanka Stamova

doi:10.3934/mmc.2021003

Mathematical Modelling and Control

2021, Volume 1, Issue 1: 26-34. doi: 10.3934/mmc.2021003

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Research article

Practical exponential stability with respect to $ h- $manifolds of discontinuous delayed Cohen–Grossberg neural networks with variable impulsive perturbations

1.
Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
2.
Department of Computer Sciences, Technical University of Sofia, Sliven 8800, Bulgaria

Received: 21 February 2021 Accepted: 09 March 2021 Published: 15 March 2021

In the present work, we study discontinuous impulsive systems of the type of Cohen-Grossberg Neural Networks (CGNNs) with time-varying delays. The impulsive perturbations are realized not at fixed moments of time, and can be considered as control inputs. The hybrid concept of practical exponential stability with respect to specific manifolds defined by a function is introduced and studied analytically. The established results are applied to the case of Bidirectional Associative Memory (BAM) CGNNs. Lyapunov function method and the Razumikhin technique are the base of the proofs. A numerical example is also presented to demonstrate the applicability and effectiveness of the obtained stability conditions. The proposed results extend and complement some existing stability criteria for impulsive CGNNs with time-varying delays.
- Cohen–Grossberg neural networks,
- practical exponential stability,
- $ h- $manifold,
- variable impulsive perturbations,
- time-varying delays
Citation: Gani Stamov, Ekaterina Gospodinova, Ivanka Stamova. Practical exponential stability with respect to $ h- $manifolds of discontinuous delayed Cohen–Grossberg neural networks with variable impulsive perturbations[J]. Mathematical Modelling and Control, 2021, 1(1): 26-34. doi: 10.3934/mmc.2021003

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Abstract

In the present work, we study discontinuous impulsive systems of the type of Cohen-Grossberg Neural Networks (CGNNs) with time-varying delays. The impulsive perturbations are realized not at fixed moments of time, and can be considered as control inputs. The hybrid concept of practical exponential stability with respect to specific manifolds defined by a function is introduced and studied analytically. The established results are applied to the case of Bidirectional Associative Memory (BAM) CGNNs. Lyapunov function method and the Razumikhin technique are the base of the proofs. A numerical example is also presented to demonstrate the applicability and effectiveness of the obtained stability conditions. The proposed results extend and complement some existing stability criteria for impulsive CGNNs with time-varying delays.

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