Finite-time stabilization control for discontinuous time-delayed networks: New switching design

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• 作者：Ling-Ling Zhang^a ; ^b ; ^{linglingmath@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Li-Hong Huang^c ; ^{lhhuang@hnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Zuo-Wei Cai^a ; ^{caizuowei01@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Time-delayed neural networks ; Kakutani&rsquo ; s fixed point theorem ; Discontinuous activation ; Differential inclusions ; Finite-time stabilization ; Switching controller
• 刊名：Neural Networks
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：75
• 期：Complete
• 页码：84-96
• 全文大小：571 K

文摘

This paper discusses the finite-time stabilization problem for time-varying delayed neural networks (DNNs) with discontinuous activation functions. By using fixed point theory and set-valued analysis, we establish the existence theorem of equilibrium point. In order to stabilize the states of this class of discontinuous DNNs in finite time, we design two different kinds of switching controllers which are described by discontinuous functions. Under the framework of Filippov solutions, several new and effective criteria are derived to realize finite-time stabilization of discontinuous DNNs based on the famous finite-time stability theory. Besides, the upper bounds of the settling time of stabilization are estimated. Numerical examples are finally provided to illustrate the correctness of the proposed design method and theoretical results.