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arXiv · 1309.1790

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

Leonid Berezansky·Elena Braverman·Lev Idels
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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.

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Leonid Berezansky, Elena Braverman, Lev Idels. 2013-09-06. New Global Exponential Stability Criteria for Nonlinear Delay Differential Systems with Applications to BAM Neural Networks. https://arxiv.org/abs/1309.1790

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