title: Finite-time stabilization control for discontinuous time-delayed networks: New switching design.
abstract: 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.
authors.affiliation: Department of Information Technology, Hunan Women's University, Changsha, Hunan 410002, China; College of Science, National University of Defense Technology, Changsha, Hunan 410073, China. Electronic address: linglingmath@gmail.com.
authors.forename: Ling-Ling
authors.initials: LL
authors.lastname: Zhang
authors.affiliation: School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan 410114, China. Electronic address: lhhuang@hnu.edu.cn.
authors.forename: Li-Hong
authors.initials: LH
authors.lastname: Huang
authors.affiliation: Department of Information Technology, Hunan Women's University, Changsha, Hunan 410002, China. Electronic address: caizuowei01@126.com.
authors.forename: Zuo-Wei
authors.initials: ZW
authors.lastname: Cai
mesh_terms: D000465:Algorithms; D020342:Finite Element Analysis; D016571:Neural Networks, Computer; D013997:Time Factors
keywords: Differential inclusions; Discontinuous activation; Finite-time stabilization; Kakutani’s fixed point theorem; Switching controller; Time-delayed neural networks