A new judgment theorem for predefined‐time stability and its application in the synchronization analysis of neural networks

Abstract

Compared with finite‐time/fixed‐time stability, predefined‐time (PDT) stability has some obvious advantages, so it is expected to be the next hot topic. The study of PDT stability depends heavily on the judgment theorems for PDT stability. However, all the existing judgment theorems for PDT stability have several drawbacks, such as complicated judging conditions and strict parameter selection. In this article, a new judgment theorem for PDT stability is proposed to fill the gap, and it is based on a very concise judging condition. To verify the usability of the new judgment theorem, we devise a matching PDT controller, and analyze the PDT synchronization of neural networks by means of the novel judgment theorem. We derive several PDT synchronization criteria, which guarantee the considered neural networks can reach PDT synchronization within an arbitrary preassigned time. The preassigned time can be set as a specific parameter in the devised controller, and the other controller parameters can also be selected easily. Lastly, we provide some confirmatory numerical simulations.

A Simplified Controller Design for Fixed/Preassigned-Time Synchronization of Stochastic Discontinuous Neural Networks

“…On the other hand, the initial state may change rapidly or cannot be measured in practical applications, so the stochastic finite-time result is hard to estimate the exact settling time. Therefore, it is indispensable to derive the sufficient conditions for FxTS and obtain settling time in (23) or (24).…”

“…Considering the above limitations, the preassigned-time synchronization (PTS) was put forward, meant to specify the settling time of synchronization as an a priori explicit value [22,23]. Up to now, PTS-related research is in full swing and has been applied in engineering cases [24][25][26]. In [24], the preassigned time was designed as a complex function for specific parameters in the PTS controller.…”

“…Up to now, PTS-related research is in full swing and has been applied in engineering cases [24][25][26]. In [24], the preassigned time was designed as a complex function for specific parameters in the PTS controller. In [25], a pure power-low controller was designed to achieve PTS.…”

Fixed‐time synchronization and energy cost estimation of delayed coupled neural networks

“…As a result, more and more academics have been starting to investigate NNs dynamics with time delays. [7][8][9][10][11][12][13][14] In practical applications, some tasks require multiple NNs to work together. 15,16 Hence, delayed coupled NNs have gained considerable attention.…”

“…However, due to the slow pace of signal propagation and amplifier switching, delay is unavoidable in the system. As a result, more and more academics have been starting to investigate NNs dynamics with time delays 7–14 …”