Robust Stability of Markovian Jump Stochastic Neural Networks with Time Delays in the Leakage Terms

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• 作者：Quanxin Zhu (1)
  Jinde Cao (2) (4)
  Tasawar Hayat (3) (4)
  Fuad Alsaadi (5)
  
  1. School of Mathematical Sciences and Institute of Finance and Statistics ; Nanjing Normal University ; Nanjing聽 ; 210023 ; Jiangsu ; China
  2. Department of Mathematics and Research Center for Complex Systems and Network Sciences ; Southeast University ; Nanjing聽 ; 210096 ; Jiangsu ; China
  4. Department of Mathematics ; Faculty of Science ; King Abdulaziz University ; Jeddah ; Saudi Arabia
  3. Department of Mathematics ; Quaid-I-Azam University ; Islamabad聽 ; 44000 ; Pakistan
  5. Department of Electrical and Computer Engineering ; Faculty of Engineering ; King Abdulaziz University ; Jeddah ; Saudi Arabia
  
• 关键词：Exponential stability ; Stochastic neural network ; Lyapunov functional ; Linear matrix inequality ; Markovian jump parameter ; Leakage time delay
• 刊名：Neural Processing Letters
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：41
• 期：1
• 页码：1-27
• 全文大小：425 KB
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• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Complexity
  Artificial Intelligence and Robotics
  Electronic and Computer Engineering
  Operation Research and Decision Theory
  
• 出版者：Springer Netherlands
• ISSN：1573-773X

文摘

This paper deals with the problem of exponential stability for a class of Markovian jump stochastic neural networks with time delays in the leakage terms and mixed time delays. The jumping parameters are modeled as a continuous-time, finite-state Markov chain, and the mixed time delays consist of time-varying delays and distributed delays. By using the method of model transformation, Lyapunov stability theory, stochastic analysis and linear matrix inequalities techniques, several novel sufficient conditions are derived to guarantee the exponential stability in the mean square of the equilibrium point of the suggested system in two cases: with known or unknown parameters. Moreover, some remarks and discussions are given to illustrate that the obtained results are significant, which comprises and generalizes those obtained in the previous literature. In particular, the obtained stability conditions are delay-dependent, which depends on all the delay constants, and thus the presented results are less conservatism. Finally, two numerical examples are provided to show the effectiveness of the theoretical results.