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**Robust stability analysis of generalized neural networks with discrete and distributed time delays.**
*(English)*
Zbl 1142.93401

Summary: This paper is concerned with the problem of robust global stability analysis for generalized neural networks (GNNs) with both discrete and distributed delays. The parameter uncertainties are assumed to be time-invariant and bounded, and belong to given compact sets. The existence of the equilibrium point is first proved under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, by employing a Lyapunov-Krasovskii functional, the addressed stability analysis problem is converted into a convex optimization problem, and a linear matrix inequality (LMI) approach is utilized to establish the sufficient conditions for the globally robust stability for the GNNs, with and without parameter uncertainties. These conditions can be readily checked by utilizing the Matlab LMI toolbox. A numerical example is provided to demonstrate the usefulness of the proposed global stability condition.

### MSC:

93D09 | Robust stability |

34K20 | Stability theory of functional-differential equations |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

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\textit{Z. Wang} et al., Chaos Solitons Fractals 30, No. 4, 886--896 (2006; Zbl 1142.93401)

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