221 research outputs found
Recommended from our members
Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays
Copyright [2006] 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 global asymptotic stability analysis problem is considered for a class of stochastic Cohen-Grossberg neural networks with mixed time delays, which consist of both the discrete and distributed time delays. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, a linear matrix inequality (LMI) approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square. It is shown that the addressed stochastic Cohen-Grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two LMIs are feasible, where the feasibility of LMIs can be readily checked by the Matlab LMI toolbox. It is also pointed out that the main results comprise some existing results as special cases. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria
Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays
This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdIn this paper, the problem of stability analysis for a class of impulsive stochastic Cohen–Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic Cohen–Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.This work was supported by the Natural Science Foundation of CQ CSTC under grant 2007BB0430, the Scientific Research Fund of Chongqing Municipal Education Commission under Grant KJ070401, 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
Asymptotic stability for neural networks with mixed time-delays: The discrete-time case
This is the post print version of the article. The official published version can be obtained from the link - Copyright 2009 Elsevier LtdThis 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.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
Discrete-time recurrent neural networks with time-varying delays: Exponential stability analysis
This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier LtdThis Letter is concerned with the analysis problem of exponential stability for a class of discrete-time recurrent neural networks (DRNNs) with time delays. The delay is of the time-varying nature, and the activation functions are assumed to be neither differentiable nor strict monotonic. Furthermore, the description of the activation functions is more general than the recently commonly used Lipschitz conditions. Under such mild conditions, we first prove the existence of the equilibrium point. Then, by employing a Lyapunov–Krasovskii functional, a unified linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the DRNNs to be globally exponentially stable. It is shown that the delayed DRNNs are globally exponentially stable if a certain LMI is solvable, where the feasibility of such an LMI 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.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the Alexander von Humboldt Foundation of Germany, the Natural Science Foundation of Jiangsu Education Committee of China (05KJB110154), the NSF of Jiangsu Province of China (BK2006064), and the National Natural Science Foundation of China (10471119)
Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays
Copyright [2009] 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 paper, we introduce a new class of discrete-time neural networks (DNNs) with Markovian jumping parameters as well as mode-dependent mixed time delays (both discrete and distributed time delays). Specifically, the parameters of the DNNs are subject to the switching from one to another at different times according to a Markov chain, and the mixed time delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. We first deal with the stability analysis problem of the addressed neural networks. A special inequality is developed to account for the mixed time delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the stochastic stability. We then turn to the synchronization problem among an array of identical coupled Markovian jumping neural networks with mixed mode-dependent time delays. By utilizing the Lyapunov stability theory and the Kronecker product, it is shown that the addressed synchronization problem is solvable if several LMIs are feasible. Hence, different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation, where the LMIs can be easily solved by using the available Matlab LMI toolbox. Two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained
pth moment exponential stability of stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays
In this paper, stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are investigated. By using Lyapunov function and the Ito differential formula, some sufficient conditions for the pth moment exponential stability of such stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are established. An example is given to illustrate the feasibility of our main theoretical findings. Finally, the paper ends with a brief conclusion. Methodology and achieved results is to be presented
Global exponential convergence of delayed inertial Cohen–Grossberg neural networks
In this paper, the exponential convergence of delayed inertial Cohen–Grossberg neural networks (CGNNs) is studied. Two methods are adopted to discuss the inertial CGNNs, one is expressed as two first-order differential equations by selecting a variable substitution, and the other does not change the order of the system based on the nonreduced-order method. By establishing appropriate Lyapunov function and using inequality techniques, sufficient conditions are obtained to ensure that the discussed model converges exponentially to a ball with the prespecified convergence rate. Finally, two simulation examples are proposed to illustrate the validity of the theorem results
Recommended from our members
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
Exponential synchronization for reaction-diffusion neural networks with mixed time-varying delays via periodically intermittent control
This paper deals with the exponential synchronization problem for reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance. By using stochastic analysis approaches and constructing a novel Lyapunov–Krasovskii functional, a periodically intermittent controller is first proposed to guarantee the exponential synchronization of reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance in terms of p-norm. The obtained synchronization results are easy to check and improve upon the existing ones. Particularly, the traditional assumptions on control width and time-varying delays are removed in this paper. This paper also presents two illustrative examples and uses simulated results of these examples to show the feasibility and effectiveness of the proposed scheme
- …