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global exponential stability of mixed discrete and distributively delayed cellular neural network

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Chinese Physics B 2011年第1期20卷 245-257页

作者：姚洪兴周佳燕 Nonlinear Scientific Research Center Jiangsu University

This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point, then by employing the Lyapunov-Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays, in addition, the example is provided to illustrate the applicability of the result.

关键词： global exponential stability cellular neural network mixed discrete and distributed de-lays Lyapunov-Krasovskii functional and Young inequality

global exponential stability IN HOPFIELD AND BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH TIME DELAYS

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Chinese Annals of Mathematics,Series B 2004年第2期25卷 255-262页

作者： RONGLIBIN LUWENLIAN CHENTIANPING LaboratoryofNonlinearScience InstituteofMathematicsFudanUniversityShanghai200433China. DepartmentofMathematics andLaboratoryofNonlinearScienceInstituteofMathematicsFudanUniversityShanghai200433China.

Without assuming the boundedness, strict monotonicity and differentiability of the activation functions, the authors utilize the Lyapunov functional method to analyze the global convergence of some delayed models. For the Hopfield neural network with time delays, a new sufficient condition ensuring the existence, uniqueness and global exponential stability of the equilibrium point is derived. This criterion concerning the signs of entries in the connection matrix imposes constraints on the feedback matrix independently of the delay parameters. From a new viewpoint, the bidirectional associative memory neural network with time delays is investigated and a new global exponential stability result is given.

关键词： Hopfield neural network Bidirectional associative memory (BAM) global exponential stability Time delays Lyapunov functional

global exponential stability of switched systems

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Applied Mathematics and Mechanics(English Edition) 2011年第9期32卷 1197-1206页

作者： V.FILIPOVIC Faculty of Mechanical Engineering University of KragujevacDositejeva 19Kraljevo 36000Serbia

This paper proposes a method for the stability analysis of deterministic switched *** motivational examples are introduced （nonholonomic system and constrained pendulum）.The finite collection of models consists of nonlinear models,and a switching sequence is *** is supposed that there is no jump in the state at switching instants,and there is no Zeno behavior,i.e.,there is a finite number of switches on every bounded *** the analysis of deterministic switched systems,the multiple Lyapunov functions are used,and the global exponential stability is *** exponentially stable equilibrium of systems is relevant for practice because such systems are robust to perturbations.

关键词： switched system multiple Lyapunov function global exponential stability

global exponential stability for delayed cellular neural networks and estimate of exponential convergence rate

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Journal of Systems Engineering and Electronics 2004年第3期15卷 344-349页

作者：张强马润年许进 SchoolofMechanicalEngineering DalianUniversityofTechnologyDalian116024P.R.China AdvancedDesignTechnologyCenter DalianUniversityDalian116622P.R.China SchoolofManagement Xi'anJiaotongUniversityXi'an710049P.R.China

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.

关键词： global exponential stability convergence rate cellular neural networks with delay delay differential inequality.

New results on global exponential stability of competitive neural networks with different time scales and time-varying delays

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Chinese Physics B 2008年第5期17卷 1670-1677页

作者：崔宝同陈君楼旭阳 Research Center of Control Science and Engineering Jiangnan University

This paper studies the global exponential stability of competitive neural networks with different time scales and time-varying delays. By using the method of the proper Lyapunov functions and inequality technique, some sufficient conditions are presented for global exponential stability of delay competitive neural networks with different time scales. These conditions obtained have important leading significance in the designs and applications of global exponential stability for competitive neural networks. Finally, an example with its simulation is provided to demonstrate the usefulness of the proposed criteria.

关键词： competitive neural network different time scale global exponential stability delay

global ATTRACTIVITY AND global exponential stability FOR DELAYED HOPFIELD NEURAL NETWORK MODELS

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Applied Mathematics and Mechanics(English Edition) 2001年第6期22卷 711-716页

作者：蒲志林徐道义 Department of Mathematics Sichuan Normal UniversityChengdu 610066P R China Department of Mathematics Sichuan UniversityChengdu 610064P R China

Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.

关键词： neural networks global attractivity global exponential stability

Existence and global exponential stability of Pseudo Almost Periodic Solutions of a General Delayed BAM Neural Networks

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Journal of Systems Science & Complexity 2018年第3期31卷 608-620页

作者： DUAN Lian School of Mathematics and Big Data Anhui University of Science and Technology

This paper studies a class of general BAM neural networks with multiple delays. Em- ploying the exponential dichotomy theory and fixed point method, together with constructing suitable Lyapunov functionals, easily verifiable delay-independent criteria are established to ensure the exis- tence and global exponential stability of pseudo almost periodic solutions, which not only generalize but also complement some existing ones. These theoretical results are also supported with numerical simulations.

关键词： General BAM neural network global exponential stability pseudo almost periodic solu-tion

ROBUST global exponential stability OF UNCERTAIN IMPULSIVE SYSTEMS

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Acta Mathematica Scientia 2005年第1期25卷 161-169页

作者：刘斌刘新芝廖晓昕 Department of Information and Computation Science Zhuzhou Institute of Technology Zhuzhou 412008 China Department of Control Science and Engineering Huazhong University of Science and Technology Wuhan 430074 China Department of Control Science and EngineeringHuazhong University of Science and Technology Wuhan 430074t China Department of Applied Mathematics University of Waterloo Waterloo Ontario N2L 3G1 Canada Department of Control Science and Engineering Huazhong University of Science and Technology Wuhan 430074 China

By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.

关键词： Uncertain impulsive system interval matrix Riccati/Hamilton-Jacobi inequality global exponential stability robust global exponential stability

global exponential stability of cellular neural networks with multi-proportional delays

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International Journal of Biomathematics 2015年第6期8卷 1-17页

作者： Liqun Zhou Yanyan Zhang School of Mathematics Science Tianjin Normal University Tianjin 300387 P. R. China

In this paper, a class of cellular neural networks （CNNs） with multi-proportional delays is studied. The nonlinear transformation yi（t） = xi（et） transforms a class of CNNs with multi-proportional delays into a class of CNNs with multi-constant delays and time- varying coefficients. By applying Brouwer fixed point theorem and constructing the delay differential inequality, several delay-independent and delay-dependent sufficient conditions are derived for ensuring the existence, uniqueness and global exponential stability of equilibrium of the system and the exponentially convergent rate is estimated. And several examples and their simulations are given to illustrate the effectiveness of obtained results.

关键词： Cellular neural networks proportional delay global exponential stability Brouwer fixed point theorem delay differential inequality.