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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
Issue 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
ISSN: 0893-6080
Appears in Collections:Computer Science
Dept of Computer Science Research Papers

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