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Delay-dependent exponential stability for a class of neural networks with time delays. (English) Zbl 1097.34057
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 τ is the delay parameter, it is proved that the origin is globally exponentially stable for any 0<τ<τ ¯ if a suitable linear matrix inequality (LMI) is verified. Such LMI can be checked numerically and the upper bound τ ¯ can be computed explicitly by solving a quasi-convex matrix optimization problem. Two illustrative examples show the practical applicability of the criterion.
34K20Stability theory of functional-differential equations
92D20Protein sequences, DNA sequences