Journal
NEURAL NETWORKS
Volume 22, Issue 1, Pages 67-74Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.neunet.2008.10.001
Keywords
Discrete-time neural networks; Stochastic neural networks; Asymptotic stability; Discrete time-delays; Distributed time-delays; Lyapunov-Krasovskii functional; Linear matrix inequality
Funding
- Biotechnology and Biological Sciences Research Council (BBSRC) of the UK [BB/C506264/1, 100/EGM17735]
- Engineering and Physical Sciences Research Council (EPSRC) of the UK [GR/S27658/01, EP/C524586/1]
- Royal Society of the UK
- Natural Science Foundation of jiangsu Province of China [BK2007075]
- National Natural Science Foundation of China [60774073]
- Alexander von Humboldt Foundation of Germany
- Biotechnology and Biological Sciences Research Council [BB/C506264/1] Funding Source: researchfish
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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. (C) 2008 Elsevier Ltd. All rights reserved.
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