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

2013/09/06 by Leonid Berezansky, Berezansky, Leonid, Elena Braverman +3
Computer Science · Engineering · #34K11 #34K20 #34K25 #92D25 #Advanced Research in Systems and Signal Processing #Dynamical Systems (math.DS) #FOS: Mathematics #Neural Networks Stability and Synchronization #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.1309.1790

openalex publication_date 2013/09/06 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We consider a nonlinear non-autonomous system with time-varying delays \n
dotx_i(t)=-a_i(t)x_i(h_i(t))+
sum_j=1^mF_ij(t,x_j(g_ij(t))) which\nhas a large number of applications in the theory of artificial neural networks.\nVia the M-matrix method, easily verifiable sufficient stability conditions for\nthe nonlinear system and its linear version are obtained. Application of the\nmain theorem requires just to check whether a matrix, which is explicitly\nconstructed by the system's parameters, is an M-matrix. Comparison with the\ntests obtained by K. Gopalsamy (2007) and B. Liu (2013) for BAM neural networks\nillustrates novelty of the stability theorems. Some open problems conclude the\npaper.\n

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