Global convergence of neural networks with mixed time-varying delays and discontinuous neuron activations

Authors:
Jun Liu;Xinzhi Liu;Wei-Chau Xie
Affiliations:
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1;Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1;Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Venue:
Information Sciences: an International Journal
Year:
2012

Citing 16
Cited 9

Topics in matrix analysis

Topics in matrix analysis
Functional differential equations with infinite delay

Functional differential equations with infinite delay
Neural Networks: A Comprehensive Foundation

Neural Networks: A Comprehensive Foundation
A fast learning algorithm for time-delay neural networks

Information Sciences—Applications: An International Journal
Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions

Neural Networks
Combining Feature Reduction and Case Selection in Building CBR Classifiers

IEEE Transactions on Knowledge and Data Engineering
Dynamical Behaviors of Delayed Neural Network Systems with Discontinuous Activation Functions

Neural Computation
Almost periodic dynamics of a class of delayed neural networks with discontinuous activations

Neural Computation
pth moment stability analysis of stochastic recurrent neural networks with time-varying delays

Information Sciences: an International Journal
Robust Stability Criterion for Delayed Neural Networks with Discontinuous Activation Functions

Neural Processing Letters
Global stability analysis of a general class of discontinuous neural networks with linear growth activation functions

Information Sciences: an International Journal
Robust exponential stability criterion for uncertain neural networks with discontinuous activation functions and time-varying delays

Neurocomputing
Global stability analysis in Cohen-Grossberg neural networks with delays and inverse Hölder neuron activation functions

Information Sciences: an International Journal
Passive learning and input-to-state stability of switched Hopfield neural networks with time-delay

Information Sciences: an International Journal
Global exponential stability of the periodic solution of delayed Cohen-Grossberg neural networks with discontinuous activations

Neurocomputing
Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain

IEEE Transactions on Neural Networks

Global exponential synchronization of generalized stochastic neural networks with mixed time-varying delays and reaction-diffusion terms

Neurocomputing
On the periodic dynamics of a class of time-varying delayed neural networks via differential inclusions

Neural Networks
Global exponential stability of almost periodic solution of delayed neural networks with discontinuous activations

Information Sciences: an International Journal
A genetic algorithm approach to a neural-network-based inverse kinematics solution of robotic manipulators based on error minimization

Information Sciences: an International Journal
Design of a robust neural network-based tracking controller for a class of electrically driven nonholonomic mechanical systems

Information Sciences: an International Journal
On the periodic dynamics of a general Cohen-Grossberg BAM neural networks via differential inclusions

Neurocomputing
Dynamical behaviors of Cohen-Grossberg neural networks with mixed time delays and discontinuous activations

Neurocomputing
Dynamical behaviors for discontinuous and delayed neural networks in the framework of Filippov differential inclusions

Neural Networks
Periodicity and global exponential stability of generalized Cohen-Grossberg neural networks with discontinuous activations and mixed delays

Neural Networks

Quantified Score

Hi-index	0.07

Visualization

Abstract

In this paper, we investigate the dynamical behavior of a class of delayed neural networks with discontinuous neuron activations and general mixed time-delays involving both time-varying delays and distributed delays. Due to the presence of time-varying delays and distributed delays, the step-by-step construction of local solutions cannot be applied. This difficulty can be overcome by constructing a sequence of solutions to delayed dynamical systems with high-slope activations and show that this sequence converges to a desired Filippov solution of the discontinuous delayed neural networks. We then derive two sets of sufficient conditions for the global exponential stability and convergence of the neural networks, in terms of linear matrix inequalities (LMIs) and M-matrix properties (equivalently, some diagonally dominant conditions), respectively. Convergence behavior of both the neuron state and the neuron output are discussed. The obtained results extend previous work on global stability of delayed neural networks with Lipschitz continuous neuron activations, and neural networks with discontinuous neuron activations and only constant delays.