Mean-square exponential input-to-state stability of stochastic delayed neural networks

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

“…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.…”

“…However, it is unnecessary to converge to an equilibrium point in many practical systems, such as stock markets, pendulums, air temperature and finance markets. 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.…”

L2–L∞filter design for a class of neutral stochastic time delay systems

“…post-multiplying (21) in Theorem 2 by J T 2 J T 1 and its transpose respectively, and pre-and post-multiplying (22) in Theorem 2 by J T 4 J T 3 and its transpose respectively, we can obtain the linear matrix inequalities (28)- (29) in Theorem 3, respectively.…”

Piecewise pseudo-almost periodic solution for impulsive non-autonomous high-order Hopfield neural networks with variable delays

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). It is known to all that studies on neural dynamic systems not only involve a discussion of stability properties, but also involve many dynamic behaviors such as periodic oscillatory behavior, almost periodic oscillatory properties, chaos and bifurcation.…”