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
Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality (LMIs) t...Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality (LMIs) technique, delay-dependent stability criteria are derived in terms of LMIs avoiding bounding certain cross terms, which often leads to conservatism. The effectiveness of the proposed stability criteria and the improvement over the existing results are illustrated in the numerical examples.展开更多
In this paper, the problem of the global exponential stability analysis is investigated for a class of recurrent neural networks (RNNs) with time-varying discrete and distributed delays. Due to a novel technique whe...In this paper, the problem of the global exponential stability analysis is investigated for a class of recurrent neural networks (RNNs) with time-varying discrete and distributed delays. Due to a novel technique when estimating the upper bound of the derivative of Lyapunov functional, we establish new exponential stability criteria in terms of LMIs. It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to show the effectiveness of the proposed results.展开更多
In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global e...In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global exponential robust stability is presented. It is shown that the obtained result is different from or improves some existing ones reported in the literatures. Finally, some numerical examples and a simulation are given to show the effectiveness of the obtained result.展开更多
In this paper, the global asymptotic stability is investigated for a class of Cohen-Grossberg neural networks with time-varying and distributed delays. By using the Lyapunov-Krasovskii functional and equivalent descri...In this paper, the global asymptotic stability is investigated for a class of Cohen-Grossberg neural networks with time-varying and distributed delays. By using the Lyapunov-Krasovskii functional and equivalent descriptor form of the considered system, several delay-dependent sufficient conditions are obtained to guarantee the asymptotic stability of the addressed systems. These conditions are dependent on both time-varying and distributed delays and presented in terms of LMIs and therefore, the stability criteria of such systems can be checked readily by resorting to the Matlab LMI toolbox. Finally, an example is given to show the effectiveness and less conservatism of the proposed methods.展开更多
In this paper,the global robust exponential stability is considered for a class of neural networks with parametric uncer- tainties and time-varying delay.By using Lyapunov functional method,and by resorting to the new...In this paper,the global robust exponential stability is considered for a class of neural networks with parametric uncer- tainties and time-varying delay.By using Lyapunov functional method,and by resorting to the new technique for estimating the upper bound of the derivative of the Lyapunov functional,some less conservative exponential stability criteria are derived in terms of linear matrix inequalities (LMIs).Numerical examples are presented to show the effectiveness of the proposed method.展开更多
In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are e...In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are established by using the fixed point theorem and Lyapunov functional. An example is given to demonstrate the effectiveness of our results.展开更多
This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay. Some Lyapunov-KrasoVskii functi...This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay. Some Lyapunov-KrasoVskii functionals are constructed and the linear matrix inequality (LMI) approach and free weighting matrix method are employed to devise some delay-dependent stability criteria which guarantee the existence, uniqueness and global exponential stability of the equilibrium point for all admissible parametric uncertainties. By using Leibniz-Newton formula, free weighting matrices are employed to express this relationship, which implies that the new criteria are less conservative than existing ones. Some examples suggest that the proposed criteria are effective and are an improvement over previous ones.展开更多
The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differen...The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium (if it exists) is globally asymptotically stable and this implies that the equilibrium of the system is unique.展开更多
In this paper, the global stability of Takagi-Sugeno (TS) uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays (TSUSFRNNs) is considered. A novel LMI-based stabili...In this paper, the global stability of Takagi-Sugeno (TS) uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays (TSUSFRNNs) is considered. A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSUSFRNNs. The proposed stability conditions are demonstrated through numerical examples. Furthermore, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is removed. Comparison results are demonstrated to show that the proposed method is more able to guarantee the widest stability region than the other methods available in the existing literature.展开更多
This paper presents the stability analysis for a class of neural networks with time varying delays that are represented by the Takagi^ugeno IT-S) model. The main results given here focus on the stability criteria usi...This paper presents the stability analysis for a class of neural networks with time varying delays that are represented by the Takagi^ugeno IT-S) model. The main results given here focus on the stability criteria using a new Lyapunov functional. New relaxed conditions and new linear matrix inequality-based designs are proposed that outperform the previous results found in the literature. Numerical examples are provided to show that the achieved conditions are less conservative than the existing ones in the literature.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 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
The robust global exponential stability of a class of interval recurrent neural networks(RNNs) is studied,and a new robust stability criterion is obtained in the form of linear matrix inequality.The problem of robus...The robust global exponential stability of a class of interval recurrent neural networks(RNNs) is studied,and a new robust stability criterion is obtained in the form of linear matrix inequality.The problem of robust stability of interval RNNs is transformed into a problem of solving a class of linear matrix inequalities.Thus,the robust stability of interval RNNs can be analyzed by directly using the linear matrix inequalities(LMI) toolbox of MATLAB.Numerical example is given to show the effectiveness of the obtained 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
This paper investigates the global exponential stability of reaction-diffusion neural networks with discrete and distributed time-varying delays. By constructing a more general type of Lyapunov-Krasovskii functional c...This paper investigates the global exponential stability of reaction-diffusion neural networks with discrete and distributed time-varying delays. By constructing a more general type of Lyapunov-Krasovskii functional combined with a free-weighting matrix approach and analysis techniques, delay-dependent exponential stability criteria are derived in the form of linear matrix inequalities. The obtained results are dependent on the size of the time-vaxying delays and the measure of the space, which are usually less conservative than delay-independent and space-independent ones. These results are easy to check, and improve upon the existing stability results. Some remarks are given to show the advantages of the obtained results over the previous results. A numerical example has been presented to show the usefulness of the derived linear matrix inequality (LMI)-based stability conditions.展开更多
The problem of delay-dependent asymptotic stability for neurM networks with interval time-varying delay is investigated. Based on the idea of delay decomposition method, a new type of Lyapunov Krasovskii functional is...The problem of delay-dependent asymptotic stability for neurM networks with interval time-varying delay is investigated. Based on the idea of delay decomposition method, a new type of Lyapunov Krasovskii functional is constructed. Several novel delay-dependent stability criteria are presented in terms of linear matrix inequality by using the Jensen integral inequality and a new convex combination technique. Numerical examples are given to demonstrate that the proposed method is effective and less conservative.展开更多
Based on wavelet neural networks (WNNs) and recurrent neural networks (RNNs), a class of models on recurrent wavelet neural networks (RWNNs) is proposed. The new networks possess the advantages of WNNs and RNNs....Based on wavelet neural networks (WNNs) and recurrent neural networks (RNNs), a class of models on recurrent wavelet neural networks (RWNNs) is proposed. The new networks possess the advantages of WNNs and RNNs. In this paper, asymptotic stability of RWNNs is researched.according to the Lyapunov theorem, and some theorems and formulae are given. The simulation results show the excellent performance of the networks in nonlinear dynamic system recognition.展开更多
In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the ...In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the method of linear matrix inequality (LMI) and parametrized first-order model transformation, several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained. A numerical example is given to illustrate the effectiveness of our results.展开更多
In this paper, the problem of delay-distribution-dependent stability is investigated for continuous-time recurrent neural networks (CRNNs) with stochastic delay. Different from the common assumptions on time delays,...In this paper, the problem of delay-distribution-dependent stability is investigated for continuous-time recurrent neural networks (CRNNs) with stochastic delay. Different from the common assumptions on time delays, it is assumed that the probability distribution of the delay taking values in some intervals is known a priori. By making full use of the information concerning the probability distribution of the delay and by using a tighter bounding technique (the reciprocally convex combination method), less conservative asymptotic mean-square stable sufficient conditions are derived in terms of linear matrix inequalities (LMIs). Two numerical examples show that our results are better than the existing ones.展开更多
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.
文摘Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality (LMIs) technique, delay-dependent stability criteria are derived in terms of LMIs avoiding bounding certain cross terms, which often leads to conservatism. The effectiveness of the proposed stability criteria and the improvement over the existing results are illustrated in the numerical examples.
基金supported by National Natural Science Foundation of China (No.60674027,No.60974127)Key Project of Education Ministry of China (No.208074)
文摘In this paper, the problem of the global exponential stability analysis is investigated for a class of recurrent neural networks (RNNs) with time-varying discrete and distributed delays. Due to a novel technique when estimating the upper bound of the derivative of Lyapunov functional, we establish new exponential stability criteria in terms of LMIs. It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to show the effectiveness of the proposed results.
基金supported by 973 Programs (No.2008CB317110)the Key Project of Chinese Ministry of Education (No.107098)+1 种基金Sichuan Province Project for Applied Basic Research (No.2008JY0052)the Project for Academic Leader and Group of UESTC
文摘In this paper, the global exponential robust stability of neural networks with ume-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global exponential robust stability is presented. It is shown that the obtained result is different from or improves some existing ones reported in the literatures. Finally, some numerical examples and a simulation are given to show the effectiveness of the obtained result.
基金the National Natural Science Foundation of China (No.60574006).
文摘In this paper, the global asymptotic stability is investigated for a class of Cohen-Grossberg neural networks with time-varying and distributed delays. By using the Lyapunov-Krasovskii functional and equivalent descriptor form of the considered system, several delay-dependent sufficient conditions are obtained to guarantee the asymptotic stability of the addressed systems. These conditions are dependent on both time-varying and distributed delays and presented in terms of LMIs and therefore, the stability criteria of such systems can be checked readily by resorting to the Matlab LMI toolbox. Finally, an example is given to show the effectiveness and less conservatism of the proposed methods.
基金Natural Science Foundation of Henan Education Department (No.2007120005).
文摘In this paper,the global robust exponential stability is considered for a class of neural networks with parametric uncer- tainties and time-varying delay.By using Lyapunov functional method,and by resorting to the new technique for estimating the upper bound of the derivative of the Lyapunov functional,some less conservative exponential stability criteria are derived in terms of linear matrix inequalities (LMIs).Numerical examples are presented to show the effectiveness of the proposed method.
文摘In this paper, the Cohen-Grossberg neural networks with time-varying delays and impulses are considered. New sufficient conditions for the existence and global exponential stability of a unique equilibrium point are established by using the fixed point theorem and Lyapunov functional. An example is given to demonstrate the effectiveness of our results.
基金This work is supported by the National Natural Science Foundation of China (No.60674026)the Key Research Foundation of Science and Technology of the Ministry of Education of China (No.107058).
文摘This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay. Some Lyapunov-KrasoVskii functionals are constructed and the linear matrix inequality (LMI) approach and free weighting matrix method are employed to devise some delay-dependent stability criteria which guarantee the existence, uniqueness and global exponential stability of the equilibrium point for all admissible parametric uncertainties. By using Leibniz-Newton formula, free weighting matrices are employed to express this relationship, which implies that the new criteria are less conservative than existing ones. Some examples suggest that the proposed criteria are effective and are an improvement over previous ones.
基金Project supported by the National Natural Science Foundation of China (No.10571078)the Natural Science Foundation of Gansu Province of China (No.3ZX062-B25-012)
文摘The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium (if it exists) is globally asymptotically stable and this implies that the equilibrium of the system is unique.
文摘In this paper, the global stability of Takagi-Sugeno (TS) uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays (TSUSFRNNs) is considered. A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSUSFRNNs. The proposed stability conditions are demonstrated through numerical examples. Furthermore, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is removed. Comparison results are demonstrated to show that the proposed method is more able to guarantee the widest stability region than the other methods available in the existing literature.
文摘This paper presents the stability analysis for a class of neural networks with time varying delays that are represented by the Takagi^ugeno IT-S) model. The main results given here focus on the stability criteria using a new Lyapunov functional. New relaxed conditions and new linear matrix inequality-based designs are proposed that outperform the previous results found in the literature. Numerical examples are provided to show that the achieved conditions are less conservative than the existing ones in the literature.
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.
基金Supported by the Natural Science Foundation of Shandong Province (ZR2010FM038,ZR2010FL017)
文摘The robust global exponential stability of a class of interval recurrent neural networks(RNNs) is studied,and a new robust stability criterion is obtained in the form of linear matrix inequality.The problem of robust stability of interval RNNs is transformed into a problem of solving a class of linear matrix inequalities.Thus,the robust stability of interval RNNs can be analyzed by directly using the linear matrix inequalities(LMI) toolbox of MATLAB.Numerical example is given to show the effectiveness of the obtained 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 National Natural Science Foundation of China (Grant No. 60974139)partially supported by the Fundamental Research Funds for the Central Universities
文摘This paper investigates the global exponential stability of reaction-diffusion neural networks with discrete and distributed time-varying delays. By constructing a more general type of Lyapunov-Krasovskii functional combined with a free-weighting matrix approach and analysis techniques, delay-dependent exponential stability criteria are derived in the form of linear matrix inequalities. The obtained results are dependent on the size of the time-vaxying delays and the measure of the space, which are usually less conservative than delay-independent and space-independent ones. These results are easy to check, and improve upon the existing stability results. Some remarks are given to show the advantages of the obtained results over the previous results. A numerical example has been presented to show the usefulness of the derived linear matrix inequality (LMI)-based stability conditions.
基金supported by the Doctoral Startup Foundation of Taiyuan University of Science and Technology,China (Grant No. 20112010)
文摘The problem of delay-dependent asymptotic stability for neurM networks with interval time-varying delay is investigated. Based on the idea of delay decomposition method, a new type of Lyapunov Krasovskii functional is constructed. Several novel delay-dependent stability criteria are presented in terms of linear matrix inequality by using the Jensen integral inequality and a new convex combination technique. Numerical examples are given to demonstrate that the proposed method is effective and less conservative.
文摘Based on wavelet neural networks (WNNs) and recurrent neural networks (RNNs), a class of models on recurrent wavelet neural networks (RWNNs) is proposed. The new networks possess the advantages of WNNs and RNNs. In this paper, asymptotic stability of RWNNs is researched.according to the Lyapunov theorem, and some theorems and formulae are given. The simulation results show the excellent performance of the networks in nonlinear dynamic system recognition.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60604007 and 50775226)
文摘In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the method of linear matrix inequality (LMI) and parametrized first-order model transformation, several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained. A numerical example is given to illustrate the effectiveness of our results.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61273164,61034005,and 60974071)the National High Technology Research and Development Program of China(Grant No.2012AA040104)the Fundamental Research Funds for the Central Universities(Grant Nos.N100104102 and N110604007)
文摘In this paper, the problem of delay-distribution-dependent stability is investigated for continuous-time recurrent neural networks (CRNNs) with stochastic delay. Different from the common assumptions on time delays, it is assumed that the probability distribution of the delay taking values in some intervals is known a priori. By making full use of the information concerning the probability distribution of the delay and by using a tighter bounding technique (the reciprocally convex combination method), less conservative asymptotic mean-square stable sufficient conditions are derived in terms of linear matrix inequalities (LMIs). Two numerical examples show that our results are better than the existing ones.