Finite-time boundedness and stabilization of uncertain switched delayed neural networks of neutral type

Fixed-Time Stabilization of Discontinuous Neutral Neural Networks With Proportional Delays via New Fixed-Time Stability Lemmas

When studying the stability of time-delayed discontinuous systems, Lyapunov-Krasovskii functional (LKF) is an essential tool. More relaxed conditions imposed on the LKF are preferred and can take more advantages in real applications. In this article, novel conditions imposed on the LKF are first given which are different from the previous ones. New fixed-time (FXT) stability lemmas are established using some inequality techniques which can greatly extend the pioneers. The new estimations of the settling times (STs) are also obtained. For the purpose of examining the applicability of the new FXT stability lemmas, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is formulated which is more generalized than the existing ones. Using differential inclusions theory, set-valued map, and the newly obtained FXT stability lemma, some algebraic FXT stabilization criteria are derived. Finally, examples are given to show the correctness of the established results.

Prefixed-Time Local Intermittent Sampling Synchronization of Stochastic Multicoupling Delay Reaction-Diffusion Dynamic Networks

This article focuses on the problem of prefixed-time synchronization for stochastic multicoupled delay dynamic networks with reaction-diffusion terms and discontinuous activation by means of local intermittent sampling control. Notably, unlike the existing common fixed-time synchronization, this article puts forward a new synchronization concept, prefixed-time synchronization, based on the fact that stochastic noise and discontinuous activation can be seen everywhere in practical engineering, which can effectively perfect and improve the existing works. Specifically, a local intermittent in the time domain and point sampling control strategy in the spatial domain is proposed instead of a simple single intermittent control approach, which greatly reduces the control cost. In addition, by some effective means, including the famous Young's inequality, Jensen's inequality, and Hölder's inequality, we obtain two different synchronization criteria of the networks without delay and with multicoupling delays and deeply reveal the quantitative relationship among control period, point sampling length, and network scale. Finally, a numerical example is given to verify the effectiveness of the developed method and the practicability by Chua's circuit model.