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Title: Asymptotic stability for neural networks with mixed time-delays: The discrete-time case
Authors: Liu, Y
Wang, Z
Liu, X
Keywords: Discrete-time neural networks
Stochastic neural networks
Asymptotic stability
Discrete time-delays
Distributed time-delays
Lyapunov–Krasovskii functional
Linear matrix inequality
Publication Date: 2009
Publisher: Elsevier
Citation: Neural Networks, 22(1): 67-74, Jan 2009
Abstract: This paper is concerned with the stability analysis problem for a new class of discrete-time recurrent neural networks with mixed time-delays. The mixed time-delays that consist of both the discrete and distributed time-delays are addressed, for the first time, when analyzing the asymptotic stability for discrete-time neural networks. The activation functions are not required to be differentiable or strictly monotonic. The existence of the equilibrium point is first proved under mild conditions. By constructing a new Lyapnuov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the discrete-time neural networks to be globally asymptotically stable. As an extension, we further consider the stability analysis problem for the same class of neural networks but with state-dependent stochastic disturbances. All the conditions obtained are expressed in terms of LMIs whose feasibility can be easily checked by using the numerically efficient Matlab LMI Toolbox. A simulation example is presented to show the usefulness of the derived LMI-based stability condition.
Description: This is the post print version of the article. The official published version can be obtained from the link - Copyright 2009 Elsevier Ltd
Sponsorship: This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the UK under Grants BB/C506264/1 and 100/EGM17735, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grants GR/S27658/01 and EP/C524586/1, an International Joint Project sponsored by the Royal Society of the UK, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, the National Natural Science Foundation of China under Grant 60774073, and the Alexander von Humboldt Foundation of Germany.
ISSN: 0893-6080
Appears in Collections:Computer Science
Dept of Computer Science Research Papers

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