Mean-square exponential input-to-state stability of stochastic recurrent neural networks with multi-proportional delays

Abstract

This paper investigates mean-square exponential input-to-state stability of stochastic recurrent neural networks with multi-proportional delays. Here, we study the proportional delay, which is a kind of unbounded time-varying delay in stochastic recurrent neural networks, by employing Lyapunov-Krasovskii functional, stochastic analysis theory and Itô ′ s formula. A new stability criterion about the mean-square exponential input-to-state stability, which is different from the traditional stability criteria, is presented. In addition, the new proposed criterion easy to verify and less conservation than earlier publications about mean-square exponential inputto-state stability of stochastic recurrent neural networks. Finally, several examples and their simulations are given to illustrate the correctness and effectiveness of the theoretical results.

New result on the mean-square exponential input-to-state stability of stochastic delayed recurrent neural networks

“…Furthermore, two numerical examples and their simulations have been presented to demonstrate the theoretical results. Considering the work of Zhou and Liu (2017), we will study the mean-square exponential input-to-state stability for SDRNNs with timevarying coefficients and multi-proportional delays, which is an interesting and challenging task.…”

“…To the best of our knowledge, this is the first time there has been a focus on the meansquare exponential input-to-state stability of the trivial solution for SDRNNs with time-varying coefficients. We find that all results obtained in Rakkiyappan and Balasubramaniam (2008), Balasubramaniam and Rakkiyappan (2008), Chen et al (2014), Meng et al (2011), Chen et al (2018, Peng and Huang (2008), Huang et al (2008), Yu and Cao (2007), , Zhu and Cao (2014), Zhou and Liu (2017), Zhu and Shen (2013), Yang et al (2014) are concerned with SDRNNs with constant coefficients, so they are invalid for example (4.2). The method used in this paper provides an approach to analyze the mean-square exponential input-to-state stability of the trivial solution for SDRNNs with time-varying coefficients, which is the kernel of our study.…”

“…The stability problem of stochastic delayed recurrent neural networks (SDRNNs) is the most important object in the real world because such stability means that a practical system can run regularly and reliably. Fortunately, there are many published articles about stability results on SDRNNs, such as Rakkiyappan and Balasubramaniam (2008), Balasubramaniam and CONTACT Wei Chen weichen@lixin.edu.cn , Chen, Gaans, and Lunel (2014), Meng, Tian, and Hu (2011), Chen, Li, Shi, Gansa, and Lunel (2018), Peng and Huang (2008), Huang, He, and Wang (2008), Yu and Cao (2007), Zhu, Luo, and Shen (2014), Zhu and Cao (2014), Zhou and Liu (2017) and the references found in these papers. For example, the authors of Rakkiyappan and Balasubramaniam (2008), Balasubramaniam and Rakkiyappan (2008) employed a linear matrix inequality approach and Lyapunov-Krasovskii functional to study the globally asymptotic stability of SDRNNs.…”

“…Zhu and Cao presented a more general definition of stability, mean-square exponential input-to-state stability, and studied it in Zhu and Cao (2014). Three years later, Zhou and Liu (2017) studied the mean-square exponential input-to-state stability of SDRNNs with multiproportional delays. Recently, there have been some results reported on the input-to-state stability of SDRNNs (Yang, Zhou, & Huang, 2014;Zhu & Shen, 2013).…”

Mean-Square Exponential Input-to-State Stability of Stochastic Fuzzy Recurrent Neural Networks with Multiproportional Delays and Distributed Delays

“…Compared with the result in [46], our model is also more general than that in [46] since distributed delays and fuzzy factor in this paper were ignored in [46].…”