In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linea...In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linearity of output functions of neurons of the cellular neural networks. Some algebraic criteria are obtained and easily verified. Some examples are given to illustrate the correctness of the results obtained.展开更多
This paper considers adaptive synchronization of uncertain neural networks with time delays and stochastic perturbation. A general adaptive controller is designed to deal with the difficulties deduced by uncertain par...This paper considers adaptive synchronization of uncertain neural networks with time delays and stochastic perturbation. A general adaptive controller is designed to deal with the difficulties deduced by uncertain parameters and stochastic perturbations, in which the controller is less conservative and optimal since its control gains can be automatically adjusted according to some designed update laws. Based on Lyapunov stability theory and Barbalat lemma, sufficient condition is obtained for synchronization of delayed neural networks by strict mathematical proof. Moreover, the obtained results of this paper are more general than most existing results of certainly neural networks with or without stochastic disturbances. Finally, numerical simulations are presented to substantiate our theoretical results.展开更多
We investigate the stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks (MJFCNNs) with discrete, unbounded distributed delays, and the Wiener process based on sampled-d...We investigate the stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks (MJFCNNs) with discrete, unbounded distributed delays, and the Wiener process based on sampled-data control using the linear matrix inequality (LMI) approach. The Lyapunov–Krasovskii functional combined with the input delay approach as well as the free-weighting matrix approach is employed to derive several sufficient criteria in terms of LMIs to ensure that the delayed MJFCNNs with the Wiener process is stochastic asymptotical synchronous. Restrictions (e.g., time derivative is smaller than one) are removed to obtain a proposed sampled-data controller. Finally, a numerical example is provided to demonstrate the reliability of the derived results.展开更多
Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on del...Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on delay differential inequality. The method, which does not make use of any Lyapunov functional, is simple and valid for the stability analysis of neural networks with delay. Some previously established results in this paper are shown to be special casses of the presented result.展开更多
A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) + WIf(t,u(t)) + WIτf7τ(uτ(t)] dt +σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studie...A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) + WIf(t,u(t)) + WIτf7τ(uτ(t)] dt +σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.展开更多
In this paper, the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks (DNNs) with stochastic perturbation is studied. Based on the Lyapunov stability theory, stochasti...In this paper, the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks (DNNs) with stochastic perturbation is studied. Based on the Lyapunov stability theory, stochastic analysis approach and an efficient impulsive delay differential inequality, some new exponential synchronization criteria expressed in the form of the linear matrix inequality (LMI) are derived. The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square, but also can control the exponential synchronization rate. Furthermore, to estimate the stable region of the synchronization error dynamics, a novel optimization control al- gorithm is proposed, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. Simulation results finally demonstrate the effectiveness of the proposed method.展开更多
The stability of a class of delayed cellular neural networks (DCNN) with or without noise perturbation is studied. After presenting a simple and easily checkable condition for the global exponential stability of a d...The stability of a class of delayed cellular neural networks (DCNN) with or without noise perturbation is studied. After presenting a simple and easily checkable condition for the global exponential stability of a deterministic system, we further investigate the case with noise perturbation. When DCNN is perturbed by external noise, the system is globally stable. An important fact is that, when the system is perturbed by internal noise, it is globally exponentially stable only if the total noise strength is within a certain bound. This is significant since the stochastic resonance phenomena have been found to exist in many nonlinear systems.展开更多
The exponential stability of the delayed cellular neural networks (DCNN's) is investigated. By dividing the network state variables into some parts according to the characters of the neural networks, some new suffi...The exponential stability of the delayed cellular neural networks (DCNN's) is investigated. By dividing the network state variables into some parts according to the characters of the neural networks, some new sufficient conditions of exponential stability are derived via constructing a Liapunov function. It is shown that the conditions differ from previous ones. The new conditions, which are associated with some initial value, are represented by some blocks of the interconnection matrix.展开更多
This paper is concerned with a delay-dependent state estimator for neutral-type neural networks with mixed timevarying delays and Markovian jumping parameters.The addressed neural networks have a finite number of mode...This paper is concerned with a delay-dependent state estimator for neutral-type neural networks with mixed timevarying delays and Markovian jumping parameters.The addressed neural networks have a finite number of modes,and the modes may jump from one to another according to a Markov process.By construction of a suitable Lyapunov-Krasovskii functional,a delay-dependent condition is developed to estimate the neuron states through available output measurements such that the estimation error system is globally asymptotically stable in a mean square.The criterion is formulated in terms of a set of linear matrix inequalities(LMIs),which can be checked efficiently by use of some standard numerical packages.展开更多
A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks (DCNNs) is presented. It is shown that the use of a more general type of Lyapunov-Krasov...A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks (DCNNs) is presented. It is shown that the use of a more general type of Lyapunov-Krasovskii function enables the derivation of new results for an exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.展开更多
Utilizing the Liapunov functional method and combining the inequality of matrices technique to analyze the existence of a unique equilibrium point and the global asymptotic stability for delayed cellular neural networ...Utilizing the Liapunov functional method and combining the inequality of matrices technique to analyze the existence of a unique equilibrium point and the global asymptotic stability for delayed cellular neural networks (DCNNs), a new sufficient criterion ensuring the global stability of DCNNs is obtained. Our criteria provide some parameters to appropriately compensate for the tradeoff between the matrix definite condition on feedback matrix and delayed feedback matrix. The criteria can easily be used to design and verify globally stable networks. Furthermore,the condition presented here is independent of the delay parameter and is less restrictive than that given in the references.展开更多
In this paper, global asymptotic stability for cellular neural networks with time delay is discussed using a novel Liapunov function. Some novel sufficient conditions for global asymptotic stability are obtained. Thos...In this paper, global asymptotic stability for cellular neural networks with time delay is discussed using a novel Liapunov function. Some novel sufficient conditions for global asymptotic stability are obtained. Those results are simple and practical than those given by P. P. Civalleri, et al., and have a leading importance to design cellular neural networks with time delay.展开更多
The problem of passivity analysis is investigated for uncertain stochastic neural networks with discrete interval and distributed time-varying delays.The parameter uncertainties are assumed to be norm bounded and the ...The problem of passivity analysis is investigated for uncertain stochastic neural networks with discrete interval and distributed time-varying delays.The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belongs to a given interval,which means that the lower and upper bounds of interval time-varying delays are available.By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique,new delay-dependent passivity conditions are derived in terms of linear matrix inequalities(LMIs).Finally,numerical examples are given to show the less conservatism of the proposed conditions.展开更多
A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. ...A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.展开更多
In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generaliz...In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.展开更多
The cellular neural networks with delay (DCNN’s) are investigated, and some new sufficient conditions on asymptotical stability of DCNN’s are derived by constructing the Liapunov functional and utilizing M ? matrixa...The cellular neural networks with delay (DCNN’s) are investigated, and some new sufficient conditions on asymptotical stability of DCNN’s are derived by constructing the Liapunov functional and utilizing M ? matrixand theω?limit set. It is shown that the new conditions are not related to the delayed parameter.展开更多
The problem of passivity analysis for a class of discrete-time stochastic neural networks (DSNNs) with time-varying interval delay was investigated. The delay-dependent sufficient criteria were derived in terms of lin...The problem of passivity analysis for a class of discrete-time stochastic neural networks (DSNNs) with time-varying interval delay was investigated. The delay-dependent sufficient criteria were derived in terms of linear matrix inequalities (LMIs). The results are shown to be generalization of some previous results and are less conservative than the existing works. Meanwhile, the computational complexity of the obtained stability conditions is reduced because less variables are involved. A numerical example is given to show the effectiveness and the benefits of the proposed method.展开更多
A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distri...A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.展开更多
This paper is concerned with the problem of robust stability for a class of Markovian jumping stochastic neural networks (MJSNNs) subject to mode-dependent time-varying interval delay and state-multiplicative noise....This paper is concerned with the problem of robust stability for a class of Markovian jumping stochastic neural networks (MJSNNs) subject to mode-dependent time-varying interval delay and state-multiplicative noise. Based on the Lyapunov-Krasovskii functional and a stochastic analysis approach, some new delay-dependent sufficient conditions are obtained in the linear matrix inequality (LMI) format such that delayed MJSNNs are globally asymptotically stable in the mean-square sense for all admissible uncertainties. An important feature of the results is that the stability criteria are dependent on not only the lower bound and upper bound of delay for all modes but also the covariance matrix consisting of the correlation coefficient. Numerical examples are given to illustrate the effectiveness.展开更多
This paper is concerned with the problem of robust H∞ control for structured uncertain stochastic neural networks with both discrete and distributed time varying delays. A sufficient condition is presented for the ex...This paper is concerned with the problem of robust H∞ control for structured uncertain stochastic neural networks with both discrete and distributed time varying delays. A sufficient condition is presented for the existence of H∞ control based on the Lyapunov stability theory. The stability criterion is described in terms of linear matrix inequalities (LMIs), which can be easily checked in practice. An example is provided to demonstrate the effectiveness of the proposed result.展开更多
基金the National Natural Science Foundation of China (No. 10571036)Tianjin Municipal Education Commission of China(No. 20070405)
文摘In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linearity of output functions of neurons of the cellular neural networks. Some algebraic criteria are obtained and easily verified. Some examples are given to illustrate the correctness of the results obtained.
文摘This paper considers adaptive synchronization of uncertain neural networks with time delays and stochastic perturbation. A general adaptive controller is designed to deal with the difficulties deduced by uncertain parameters and stochastic perturbations, in which the controller is less conservative and optimal since its control gains can be automatically adjusted according to some designed update laws. Based on Lyapunov stability theory and Barbalat lemma, sufficient condition is obtained for synchronization of delayed neural networks by strict mathematical proof. Moreover, the obtained results of this paper are more general than most existing results of certainly neural networks with or without stochastic disturbances. Finally, numerical simulations are presented to substantiate our theoretical results.
基金the Ministry of Science and Technology of India(Grant No.DST/Inspire Fellowship/2010/[293]/dt.18/03/2011)
文摘We investigate the stochastic asymptotical synchronization of chaotic Markovian jumping fuzzy cellular neural networks (MJFCNNs) with discrete, unbounded distributed delays, and the Wiener process based on sampled-data control using the linear matrix inequality (LMI) approach. The Lyapunov–Krasovskii functional combined with the input delay approach as well as the free-weighting matrix approach is employed to derive several sufficient criteria in terms of LMIs to ensure that the delayed MJFCNNs with the Wiener process is stochastic asymptotical synchronous. Restrictions (e.g., time derivative is smaller than one) are removed to obtain a proposed sampled-data controller. Finally, a numerical example is provided to demonstrate the reliability of the derived results.
文摘Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on delay differential inequality. The method, which does not make use of any Lyapunov functional, is simple and valid for the stability analysis of neural networks with delay. Some previously established results in this paper are shown to be special casses of the presented result.
基金This project was supported by the National Natural Science Foundation of China (60074008, 60274007, 60274026) National Doctor foundaction of China (20010487005).
文摘A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) + WIf(t,u(t)) + WIτf7τ(uτ(t)] dt +σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.
基金supported by the National Natural Science Foundation of China (Grant Nos 60534010,60774048,60728307,60804006 and 60521003)the National High Technology Research and Development Program of China (Grant No 2006AA04Z183)+2 种基金Liaoning Provincial Natural Science Foundation,China (Grant No 20062018)the State Key Development Program for Basic Research of China (Grant No 2009CB320601)111 Project (Grant No B08015)
文摘In this paper, the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks (DNNs) with stochastic perturbation is studied. Based on the Lyapunov stability theory, stochastic analysis approach and an efficient impulsive delay differential inequality, some new exponential synchronization criteria expressed in the form of the linear matrix inequality (LMI) are derived. The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square, but also can control the exponential synchronization rate. Furthermore, to estimate the stable region of the synchronization error dynamics, a novel optimization control al- gorithm is proposed, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. Simulation results finally demonstrate the effectiveness of the proposed method.
基金the National Natural Science Foundation of China(No.10771155)the Special Foundation for the Authors of National Excellent Doctoral Dissertations of China(FANEDD)
文摘The stability of a class of delayed cellular neural networks (DCNN) with or without noise perturbation is studied. After presenting a simple and easily checkable condition for the global exponential stability of a deterministic system, we further investigate the case with noise perturbation. When DCNN is perturbed by external noise, the system is globally stable. An important fact is that, when the system is perturbed by internal noise, it is globally exponentially stable only if the total noise strength is within a certain bound. This is significant since the stochastic resonance phenomena have been found to exist in many nonlinear systems.
基金Supported by the National Natural Science Foundation of China (No.90208003, 30200059) and the Science and Technology Research Foundation of Education Ministry of China (No.02065)
文摘The exponential stability of the delayed cellular neural networks (DCNN's) is investigated. By dividing the network state variables into some parts according to the characters of the neural networks, some new sufficient conditions of exponential stability are derived via constructing a Liapunov function. It is shown that the conditions differ from previous ones. The new conditions, which are associated with some initial value, are represented by some blocks of the interconnection matrix.
基金Project supported by the 2010 Yeungnam University Research Grant
文摘This paper is concerned with a delay-dependent state estimator for neutral-type neural networks with mixed timevarying delays and Markovian jumping parameters.The addressed neural networks have a finite number of modes,and the modes may jump from one to another according to a Markov process.By construction of a suitable Lyapunov-Krasovskii functional,a delay-dependent condition is developed to estimate the neuron states through available output measurements such that the estimation error system is globally asymptotically stable in a mean square.The criterion is formulated in terms of a set of linear matrix inequalities(LMIs),which can be checked efficiently by use of some standard numerical packages.
基金This project was supported in part by the National Natural Science Foundation of China (60404022, 60604004)the Key Scientific Research project of Education Ministry of China (204014)the National Natural Science Foundation of China for Distinguished Young Scholars (60525303).
文摘A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks (DCNNs) is presented. It is shown that the use of a more general type of Lyapunov-Krasovskii function enables the derivation of new results for an exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.
基金ProjectsupportedbytheNationalNaturalScienceFoundationofChina (No .60 1 71 0 3 6)
文摘Utilizing the Liapunov functional method and combining the inequality of matrices technique to analyze the existence of a unique equilibrium point and the global asymptotic stability for delayed cellular neural networks (DCNNs), a new sufficient criterion ensuring the global stability of DCNNs is obtained. Our criteria provide some parameters to appropriately compensate for the tradeoff between the matrix definite condition on feedback matrix and delayed feedback matrix. The criteria can easily be used to design and verify globally stable networks. Furthermore,the condition presented here is independent of the delay parameter and is less restrictive than that given in the references.
文摘In this paper, global asymptotic stability for cellular neural networks with time delay is discussed using a novel Liapunov function. Some novel sufficient conditions for global asymptotic stability are obtained. Those results are simple and practical than those given by P. P. Civalleri, et al., and have a leading importance to design cellular neural networks with time delay.
基金supported by Department of Science and Technology,New Delhi,India(SR/S4/MS:485/07)
文摘The problem of passivity analysis is investigated for uncertain stochastic neural networks with discrete interval and distributed time-varying delays.The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belongs to a given interval,which means that the lower and upper bounds of interval time-varying delays are available.By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique,new delay-dependent passivity conditions are derived in terms of linear matrix inequalities(LMIs).Finally,numerical examples are given to show the less conservatism of the proposed conditions.
基金Project supported by the National Natural Science Foundation of China (No.60604004)the Natural Science Foundation of Hebei Province of China (No.F2007000637)the National Natural Science Foundation for Distinguished Young Scholars (No.60525303)
文摘A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.
文摘In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.
基金Supported by the the National Natural Science Foundation of China (No.90208003, 30200059) and the Science and Technology Research Foundation of Education Ministry of China (No.02065)
文摘The cellular neural networks with delay (DCNN’s) are investigated, and some new sufficient conditions on asymptotical stability of DCNN’s are derived by constructing the Liapunov functional and utilizing M ? matrixand theω?limit set. It is shown that the new conditions are not related to the delayed parameter.
基金Projects(60874030,60835001,60574006)supported by the National Natural Science Foundation of ChinaProjects(07KJB510125,08KJD510008)supported by the Natural Science Foundation of Jiangsu Higher Education Institutions of ChinaProject supported by the Qing Lan Program,Jiangsu Province,China
文摘The problem of passivity analysis for a class of discrete-time stochastic neural networks (DSNNs) with time-varying interval delay was investigated. The delay-dependent sufficient criteria were derived in terms of linear matrix inequalities (LMIs). The results are shown to be generalization of some previous results and are less conservative than the existing works. Meanwhile, the computational complexity of the obtained stability conditions is reduced because less variables are involved. A numerical example is given to show the effectiveness and the benefits of the proposed method.
基金Project supported by the National Natural Science Foundation of China (Grant No 60874113)
文摘A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.
基金supported by the National Natural Science Foundation of China (Grant Nos 60534010,60774048,60728307,60804006,60521003)the National High Technology Research and Development Program of China (863 Program) (Grant No 2006AA04Z183)+2 种基金the Natural Science Foundation of Liaoning Province of China (Grant No 20062018)973 Project (Grant No 2009CB320601)111 Project (Grant No B08015)
文摘This paper is concerned with the problem of robust stability for a class of Markovian jumping stochastic neural networks (MJSNNs) subject to mode-dependent time-varying interval delay and state-multiplicative noise. Based on the Lyapunov-Krasovskii functional and a stochastic analysis approach, some new delay-dependent sufficient conditions are obtained in the linear matrix inequality (LMI) format such that delayed MJSNNs are globally asymptotically stable in the mean-square sense for all admissible uncertainties. An important feature of the results is that the stability criteria are dependent on not only the lower bound and upper bound of delay for all modes but also the covariance matrix consisting of the correlation coefficient. Numerical examples are given to illustrate the effectiveness.
基金Project is supported in part by the National Natural Science Foundation of China (Grant No 60474031)NCET (04-0383)+2 种基金the State Key Development Program for Basic Research of China (Grant No 2002cb312200-3)the Shanghai ‘Phosphor’ Foundation(Grant No 04QMH1405)Australia-China Special Fund for Scientific & Technological Cooperation
文摘This paper is concerned with the problem of robust H∞ control for structured uncertain stochastic neural networks with both discrete and distributed time varying delays. A sufficient condition is presented for the existence of H∞ control based on the Lyapunov stability theory. The stability criterion is described in terms of linear matrix inequalities (LMIs), which can be easily checked in practice. An example is provided to demonstrate the effectiveness of the proposed result.