New Global Exponential Stability Criteria for Nonlinear Delay Differential Systems with Applications to BAM Neural Networks

Leonid Berezansky; Elena Braverman; Lev Idels

New Global Exponential Stability Criteria for Nonlinear Delay Differential Systems with Applications to BAM Neural Networks

Dynamical Systems 2013-09-10 v1

Authors: Leonid Berezansky , Elena Braverman , Lev Idels

Abstract

We consider a nonlinear non-autonomous system with time-varying delays $\dot{x_i}(t)=-a_i(t)x_{i}(h_i(t))+\sum_{j=1}^mF_{ij}(t,x_j(g_{ij}(t)))$ which has a large number of applications in the theory of artificial neural networks. Via the M-matrix method, easily verifiable sufficient stability conditions for the nonlinear system and its linear version are obtained. Application of the main theorem requires just to check whether a matrix, which is explicitly constructed by the system's parameters, is an $M$ -matrix. Comparison with the tests obtained by K. Gopalsamy (2007) and B. Liu (2013) for BAM neural networks illustrates novelty of the stability theorems. Some open problems conclude the paper.

Keywords

global exponential stability nonlinear delay differential systems BAM neural networks M-matrix method time-varying delays stability criteria non-autonomous systems

Cite

@article{arxiv.1309.1790,
  title  = {New Global Exponential Stability Criteria for Nonlinear Delay Differential Systems with Applications to BAM Neural Networks},
  author = {Leonid Berezansky and Elena Braverman and Lev Idels},
  journal= {arXiv preprint arXiv:1309.1790},
  year   = {2013}
}

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15 pages

New Global Exponential Stability Criteria for Nonlinear Delay Differential Systems with Applications to BAM Neural Networks

Abstract

Keywords

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