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Zbl 1097.34057
Xu, Shengyuan; Lam, James; Ho, Daniel W.C.; Zou, Yun
Delay-dependent exponential stability for a class of neural networks with time delays.
(English)
[J] J. Comput. Appl. Math. 183, No. 1, 16-28 (2005). ISSN 0377-0427

It is known that time delays play an important role in the dynamics of artificial neural networks, leading eventually to self-sustained oscillations and instability. This paper provides a new criterion for asymptotic stability of a nonlinear delay differential system. If $\tau$ is the delay parameter, it is proved that the origin is globally exponentially stable for any $0<\tau<\overline\tau$ if a suitable linear matrix inequality (LMI) is verified. Such LMI can be checked numerically and the upper bound $\overline\tau$ can be computed explicitly by solving a quasi-convex matrix optimization problem. Two illustrative examples show the practical applicability of the criterion.
MSC 2000:
*34K20 Stability theory of functional-differential equations
92D20 Protein sequences, DNA sequences

Keywords: Delay-dependent conditions; Global exponential stability; Linear matrix inequality; Neural networks; Neutral systems; Time-delay systems

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