

AN IMPROVED ALGEBRAIC CRITERION FOR GLOBAL EXPONENTIAL STABILITY OF RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS
Abstract
The purpose of this study was to analyze the behavior of dynamic systems under varying conditions, focusing on stability, connectivity, damping, and external disturbances. The study aimed to address key challenges in understanding how systems stabilize over time and respond to both predictable and unpredictable external factors. One major problem in such analyses lies in the inability to effectively visualize and quantify these behaviors, which this study addressed through numerical simulations and graphical representations. Using a series of well-defined equations, this study explored phenomena such as stability (f1), exponential convergence (f3), and time-shifted disturbance impacts (f9) across a time range of 0 to 10 seconds. For instance, the stability function (f1) showed a rapid decrease, stabilizing near zero within the first 4 seconds. Similarly, the exponential convergence function (f3) displayed a smooth increase, reaching 95% of its asymptotic value by 8 seconds. Other results highlighted the importance of damping, with combined stability and damping (f10) reducing oscillations significantly after 6 seconds. The findings emphasize the importance of adaptive control mechanisms and nonlinear weighting in maintaining system stability. However, the study is not without limitations. Simplified models excluded real-world noise and feedback mechanisms, making the results more theoretical than practical. Future studies should incorporate advanced modeling techniques, such as machine learning, to account for these complexities. This study contributes significantly by providing clear, graphical insights into system behaviors, enabling engineers and researchers to design more resilient systems. It is recommended that future work explore chaotic or nonlinear systems and validate these findings with real-world data. Ultimately, the study offers a practical foundation for enhancing system stability and adaptability in various fields, including control engineering and power systems.
References
H. Gao, X. Song, L. Ding, D. Liu, and M. Hao, "New conditions for global exponential stability of continuous-time neural networks with delays," Neural Computing and Applications, vol. 22, no. 1, pp. 41–48, 2013.
C. C. Hua, X. Yang, J. Yan, and X. P. Guan, "New exponential stability criteria for neural networks with time-varying delay," IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 58, no. 12, pp. 931–935, 2011.
Z. Huaguang, Y. Feisheng, L. Xiaodong, and Z. Qingling, "Stability analysis for neural networks with time-varying delay based on quadratic convex combination," IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 4, pp. 513–521, 2013.
O. M. Kwon, M. J. Park, S. M. Lee, J. H. Park, and E. J. Cha, "Stability for neural networks with time-varying delays via some new approaches," IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 2, pp. 181–193, 2013.
C. Liu, C. Li, T. Huang, and C. Li, "Stability of Hopfield neural networks with time delays and variable-time impulses," Neural Computing and Applications, vol. 22, no. 1, pp. 195–202, 2013.
G. Liu, S. X. Yang, Y. Chai, W. Feng, and W. Fu, "Robust stability criteria for uncertain stochastic neural networks of neutral-type with interval time-varying delays," Neural Computing and Applications, vol. 22, no. 2, pp. 349–359, 2013.
Y. Ma and Y. Zheng, "Stochastic stability analysis for neural networks with mixed time-varying delays," Neural Computing and Applications, vol. 26, pp. 447–455, 2015..
X. Song, H. Gao, L. Ding, D. Liu, and M. Hao, "The globally asymptotic stability analysis for a class of recurrent neural networks with delays," Neural Computing and Applications, vol. 22, no. 3-4, pp. 587–595, 2013.
X. Xie and Z. Ren, "Improved delay-dependent stability analysis for neural networks with time-varying delays," ISA Transactions, vol. 53, no. 4, pp. 1000–1005, 2014.
B. Yuhas and N. Ansari, Neural networks in telecommunications. Springer Publishing Company, New York, 2012.
Refbacks
- There are currently no refbacks.