Abstract This paper mainly studies the periodicity and exponential stability for a class of inertial neural networks (INNs) with time-varying delays. Without utilizing standard reduced-order transformation, by using the continuation theorem and Cauchy-Schwarz inequality, delay-dependent criteria shown by some algebraic inequalities are derived to ensure the existence of periodic solutions. Furthermore, by means of the fundamental inequality and constructing a modified delay-dependent Lyapunov functional, global exponential stability analysis is obtained based on the derived delay-dependent criteria. In comparison with the reduced order approach applied to the INNs and delay-independent criteria provided for the INNs in the existed literatures, the results obtained in this paper are new. Finally, numerical simulations are carried out to verify the main results.

中文翻译：

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具有时变延迟的惯性神经网络的周期性和指数稳定性的延迟相关标准

摘要 本文主要研究一类具有时变时滞的惯性神经网络(INNs)的周期性和指数稳定性。在不使用标准降阶变换的情况下，利用连续定理和Cauchy-Schwarz不等式，推导出一些代数不等式所示的时滞相关判据，以保证周期解的存在。此外，通过基本不等式，构造一个修正的时滞依赖Lyapunov泛函，基于导出的时滞依赖准则得到全局指数稳定性分析。与应用于 INN 的降阶方法和现有文献中为 INN 提供的延迟无关标准相比，本文获得的结果是新的。最后，