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**Robust almost periodic dynamics for interval neural networks with mixed time-varying delays and discontinuous activation functions.**
*(English)*
Zbl 1432.34089

Summary: The robust almost periodic dynamical behavior is investigated for interval neural networks with mixed time-varying delays and discontinuous activation functions. Firstly, based on the definition of the solution in the sense of Filippov for differential equations with discontinuous right-hand sides and the differential inclusions theory, the existence and asymptotically almost periodicity of the solution of interval network system are proved. Secondly, by constructing appropriate generalized Lyapunov functional and employing linear matrix inequality (LMI) techniques, a delay-dependent criterion is achieved to guarantee the existence, uniqueness, and global robust exponential stability of almost periodic solution in terms of LMIs. Moreover, as special cases, the obtained results can be used to check the global robust exponential stability of a unique periodic solution/equilibrium for discontinuous interval neural networks with mixed time-varying delays and periodic/constant external inputs.
Finally, an illustrative example is given to demonstrate the validity of the theoretical results.

### MSC:

34K14 | Almost and pseudo-almost periodic solutions to functional-differential equations |

93D20 | Asymptotic stability in control theory |

### Keywords:

existence; asymptotic almost periodicity; solution of interval network system; uniqueness; global robust exponential stability; almost periodic solutions
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\textit{H. Wu} et al., Abstr. Appl. Anal. 2013, Article ID 630623, 13 p. (2013; Zbl 1432.34089)

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