This work focuses on the issue of observer-based resilient dissipativity control of discrete-time memristor-based neural networks (DTMBNNs) with unbounded or bounded time-varying delays. Firstly, the Luenberger observer is designed, and additionally based on the observed states, the observer-based resilient controller is proposed. An augmented system is presented by considering both the error system and the DTMBNNs with the controller. Secondly, a novel sufficient extended exponential dissipativity condition is obtained for the augmented system with unbounded time-varying delays by proposing a system solutions-based estimation approach. This method is based on system solutions and without constructing any Lyapunov–Krasovskii functionals (LKF), thereby reducing the complexity of theoretical derivation and computational workload. In addition, an algorithm is proposed to solve the nonlinear inequalities in the sufficient condition. Thirdly, the sufficient extended exponential dissipativity condition for the augmented system with bounded time-varying delays is also obtained. Finally, the effectiveness of the theoretical results is illustrated through two simulation examples.

中文翻译：

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基于观察者的弹性耗散控制，用于具有无界或有界时变延迟的基于离散时间忆阻器的神经网络

这项工作重点关注具有无界或有界时变延迟的基于离散时间忆阻器的神经网络（DTMBNN）的基于观察者的弹性耗散控制问题。首先设计了Luenberger观测器，并根据观测状态提出了基于观测器的弹性控制器。通过考虑误差系统和带有控制器的 DTMBNN，提出了一个增强系统。其次，通过提出基于系统解的估计方法，为具有无界时变延迟的增强系统获得了一种新颖的充分扩展指数耗散条件。该方法基于系统解，无需构造任何Lyapunov-Krasovskii泛函（LKF），从而降低了理论推导的复杂度和计算工作量。此外，还提出了一种在充分条件下求解非线性不等式的算法。第三，还得到了时变有界时滞增广系统的充分扩展指数耗散条件。最后通过两个仿真算例说明了理论结果的有效性。