Exponential stability preservation in discrete-time analogues of artificial neural networks with distributed delays

Authors:
Sannay Mohamad
Affiliations:
Department of Mathematics, Faculty of Science, Universiti Brunei Darussalam, Jalan Tunku Link, Gadong BE1410, Brunei Darussalam
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 23
Cited 10

Original Contribution: Stability of fixed points and periodic orbits and bifurcations in analog neural networks

Neural Networks
Original Contribution: Associative memory with nonmonotone dynamics

Neural Networks
Discrete-time versus continuous-time models of neural networks

Journal of Computer and System Sciences
Stability in asymmetric Hopfield nets with transmission delays

Physica D
Global attractivity in delayed Hopfield neural network models

SIAM Journal on Applied Mathematics
Dynamics of a class of discete-time neural networks and their comtinuous-time counterparts

Mathematics and Computers in Simulation
Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks

Physica D
Discrete-time analogues of integrodifferential equations modelling bidirectional neural networks

Journal of Computational and Applied Mathematics
Global exponential stability of delayed Hopfield neural networks

Neural Networks
Exponential stability of continuous-time and discrete-time cellular neural networks with delays

Applied Mathematics and Computation
Exponential Periodicity of Continuous-time and Discrete-Time Neural Networks with Delays

Neural Processing Letters
Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays

Neural Networks
Some sufficient conditions for global exponential stability of delayed Hopfield neural networks

Neural Networks
Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays

Neural Networks
Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays

Journal of Computational and Applied Mathematics
Global exponential stability in DCNNs with distributed delays and unbounded activations

Journal of Computational and Applied Mathematics
Computer simulations of exponentially convergent networks with large impulses

Mathematics and Computers in Simulation
Global exponential stability of a class of neural networks with variable delays

Computers & Mathematics with Applications
Delay-dependent exponential stability for a class of neural networks with time delays

Journal of Computational and Applied Mathematics
Stability analysis of dynamical neural networks

IEEE Transactions on Neural Networks
Stability of asymmetric Hopfield networks

IEEE Transactions on Neural Networks
A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks

IEEE Transactions on Neural Networks
How delays affect neural dynamics and learning

IEEE Transactions on Neural Networks

Asymptotic stability for neural networks with mixed time-delays: The discrete-time case

Neural Networks
Delay-distribution-dependent stability of stochastic discrete-time neural networks with randomly mixed time-varying delays

Neurocomputing
Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays

IEEE Transactions on Neural Networks
Global asymptotic stability of reaction-diffusion Cohen-Grossberg neural networks with continuously distributed delays

IEEE Transactions on Neural Networks
Multiperiodicity of periodically oscillated discrete-time neural networks with transient excitatory self-connections and sigmoidal nonlinearities

IEEE Transactions on Neural Networks
An LMI approach to stability analysis of reaction-diffusion Cohen-Grossberg neural networks concerning Dirichlet boundary conditions and distributed delays

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis

Neural Networks
New delay-dependent exponential stability for discrete-time recurrent neural networks with mixed time-delays

International Journal of Innovative Computing and Applications
Letters: Further stability criteria on discrete-time delayed neural networks with distributeddelay

Neurocomputing
Letters: Triple Lyapunov functional technique on delay-dependent stability for discrete-time dynamical networks

Neurocomputing

Quantified Score

Hi-index	7.30

Visualization

Abstract

This paper demonstrates that there is a discrete-time analogue which does not require any restriction on the size of the time-step in order to preserve the exponential stability of an artificial neural network with distributed delays. The analysis exploits an appropriate Lyapunov sequence and a discrete-time system of Halanay inequalities, and also either a Young inequality or a geometric-arithmetic mean inequality, to derive several sufficient conditions on the network parameters for the exponential stability of the analogue. The sufficiency conditions are independent of the time-step, and they correspond to those that establish the exponential stability of the continuous-time network.