The neural network models with delays for solving absolute value equations

TL;DR

This paper introduces a new inverse-free neural network with delays for solving absolute value equations, demonstrating exponential convergence and effectiveness even when the inverse of matrix A has a norm greater than one.

Contribution

It proposes a novel neural network model with mixed delays for AVE, extending capabilities to cases where A^{-1} > 1, and proves exponential convergence using Lyapunov-Krasovskii theory.

Findings

Neural network models converge exponentially to the AVE solution.

Models effectively solve AVE with A^{-1} > 1.

Numerical simulations confirm the models' effectiveness.

Abstract

An inverse-free neural network model with mixed delays is proposed for solving the absolute value equation (AVE) $Ax -|x| - b =0$, which includes an inverse-free neural network model with discrete delay as a special case. By using the Lyapunov-Krasovskii theory and the linear matrix inequality (LMI) method, the developed neural network models are proved to be exponentially convergent to the solution of the AVE. Compared with the existing neural network models for solving the AVE, the proposed models feature the ability of solving a class of AVE with $\|A^{-1}\|>1$. Numerical simulations are given to show the effectiveness of the two delayed neural network models.