52 research outputs found
Global stability of a Cohen-Grossberg neural network with both time-varying and continuous distributed delays
In this paper, a generalized neural network of Cohen-Grossberg type with both discrete
time-varying and distributed unbounded delays is considered. Based on M-matrix theory, sufficient conditions are established to ensure the existence and global attractivity of an equilibrium point. The global exponential stability of the equilibrium is also addressed,
but for the model with bounded discrete time-varying delays. A comparison of results
shows that these results generalize and improve some earlier publications.Fundação para a Ciência e a Tecnologia (FCT)Universidade do Minho. Centro de Matemática (CMAT
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State estimation for delayed neural networks
Copyright [2005] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this letter, the state estimation problem is studied for neural networks with time-varying delays. The interconnection matrix and the activation functions are assumed to be norm-bounded. The problem addressed is to estimate the neuron states, through available output measurements, such that for all admissible time-delays, the dynamics of the estimation error is globally exponentially stable. An effective linear matrix inequality approach is developed to solve the neuron state estimation problem. In particular, we derive the conditions for the existence of the desired estimators for the delayed neural networks. We also parameterize the explicit expression of the set of desired estimators in terms of linear matrix inequalities (LMIs). Finally, it is shown that the main results can be easily extended to cope with the traditional stability analysis problem for delayed neural networks. Numerical examples are included to illustrate the applicability of the proposed design method
General criteria for asymptotic and exponential stabilities of neural network models with unbounded delays
For a family of differential equations with infinite delay, we give sufficient conditions for the global asymptotic, and global exponential stability of an equilibrium point. This family includes most of the delayed models of neural networks of Cohen-Grossberg type, with both bounded and unbounded distributed delay, for which general asymptotic and exponential stability criteria
are derived. As illustrations, the results are applied to several concrete models studied in the literature, and a comparison of results is given.Fundação para a Ciência e a Tecnologia (FCT) - 2009-ISFL-1-209Universidade do Minho. Centro de Matemática (CMAT
Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms
In this paper, a new global exponential stability criterion is obtained for a
general multidimensional delay difference equation using induction arguments.
In the cases that the difference equation is periodic, we prove the existence
of a periodic solution by constructing a type of Poincar\'e map. The results
are used to obtain stability criteria for a general discrete-time neural
network model with a delay in the leakage terms. As particular cases, we obtain
new stability criteria for neural network models recently studied in the
literature, in particular for low-order and high-order Hopfield and
Bidirectional Associative Memory(BAM).Comment: 20 pages, 3 figure
Stability results for impulsive functional differential equations with infinite delay
For a family of diff erential equations with in finitive delay and impulses, we establish
conditions for the existence of global solutions and for the global asymptotic and global
exponential stabilities of an equilibrium point. The results are used to give stability
criteria for a very broad family of impulsive neural network models with both unbounded
distributed delays and bounded time-varying discrete delays. Most of the impulsive
neural network models with delay recently studied are included in the general framework
presented here.Fundação para a Ciência e a Tecnologia (FCT
Existence and Global Uniform Asymptotic Stability of Pseudo Almost Periodic Solutions for Cohen-Grossberg Neural Networks with Discrete and Distributed Delays
This paper studies the existence and uniform asymptotic stability of pseudo almost periodic solutions to Cohen-Grossberg neural networks (CGNNs) with discrete and distributed delays by applying Schauder fixed point theorem and constructing a suitable Lyapunov functional. An example is given to show the effectiveness of the main results
Synchronization between Bidirectional Coupled Nonautonomous Delayed Cohen-Grossberg Neural Networks
Based on using suitable Lyapunov function and the properties of M-matrix, sufficient conditions for complete synchronization of bidirectional coupled nonautonomous Cohen-Grossberg neural networks are obtained. The methods for discussing synchronization avoid complicated error system of Cohen-Grossberg neural networks. Two numerical examples are given to show the effectiveness of the proposed synchronization method
Global asymptotic stability of nonautonomous Cohen-Grossberg neural network models with infinite delays
For a general Cohen-Grossberg neural network model with potentially unbounded time-varying
coeffi cients and infi nite distributed delays, we give su fficient conditions for its global asymptotic
stability. The model studied is general enough to include, as subclass, the most of famous
neural network models such as Cohen-Grossberg, Hopfi eld, and bidirectional associative memory.
Contrary to usual in the literature, in the proofs we do not use Lyapunov functionals. As
illustrated, the results are applied to several concrete models studied in the literature and a
comparison of results shows that our results give new global stability criteria for several neural
network models and improve some earlier publications.The second author research was suported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the "Fundacao para a Ciencia e a Tecnologia", through the project PEstOE/MAT/UI0013/2014. The authors thank the referee for valuable comments
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A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays
This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this Letter, the analysis problem for the existence and stability of periodic solutions is investigated for a class of general discrete-time recurrent neural networks with time-varying delays. For the neural networks under study, a generalized activation function is considered, and the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By employing the latest free-weighting matrix method, an appropriate Lyapunov–Krasovskii functional is constructed and several sufficient conditions are established to ensure the existence, uniqueness, and globally exponential stability of the periodic solution for the addressed neural network. The conditions are dependent on both the lower bound and upper bound of the time-varying time delays. Furthermore, the conditions are expressed in terms of the linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Two simulation examples are given to show the effectiveness and less conservatism of the proposed criteria.This work was supported in part by the National Natural Science Foundation of China under Grant 50608072, an International Joint Project sponsored by the Royal Society of the UK and the National Natural Science Foundation of China, and the Alexander von Humboldt Foundation of Germany
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