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exponential stability of cellular neural networks with multiple time delays and impulsive effects

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Chinese Physics B 2008年第11期17卷 4091-4099页

作者：李东王慧杨丹张小洪王时龙 College of Mathematics and Physics Science Chongqing University Department of Mathematics Leshan Teachers' College College of Software Engineering Chongqing University State Key Laboratories of Mechanical Transmission Chongqing University

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.

关键词： cellular neural networks (CNNs) multi-delays exponential stability linear matrix inequality (LMI)

exponential stability OF A REPARABLE MULTI-STATE DEVICE

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Journal of Systems Science & Complexity 2007年第3期20卷 437-443页

作者： Weiwei HU Houbao XU Jingyuan YU Guangtian ZHU Beijing Institute of Information and Control Beijing 100037 China. Department of Mathematics Beijing Institute of Technology Beijing 100081 China. Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China.

The exponential stability of a multi-state device is discussed in this paper. We present that the Co-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue O.

关键词： C0-semigroup exponential stability irreducibility quasi-compact.

exponential stability for cellular neural networks: an LMI approach

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Journal of Systems Engineering and Electronics 2007年第1期18卷 68-71页

作者： Liu Deyou Zhang Jianhua Guan Xinping Coll. of Science Yanshan Univ. Qinhuangdao 066004 E R. China

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.

关键词： Delayed cellular neural networks LMI Neural networks exponential stability

exponential stability of Takagi-Sugeno fuzzy systems with impulsive effects and small delays

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Chinese Physics B 2008年第3期17卷 842-846页

作者：于永斌钟其水廖晓峰虞厥邦 College of Electronic Engineering University of Electronic Science and Technology of China College of Computer Science Chongqing University

This paper deals with the exponential stability of impulsive Takagi-Sugeno fuzzy systems with delay. Impulsive control and delayed fuzzy control are applied to the system, and the criterion on exponential stability ex... 详细信息

关键词： exponential stability Takagi-Sugeno fuzzy model impulsive delay systems linear matrix inequality

exponential stability of impulsive jump linear systems with Markov process

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Journal of Systems Engineering and Electronics 2007年第2期18卷 304-310页

作者： Gao Liju Wu Yuqiang Inst. of Automation Qufu Normal Univ. Qufu 273165 P. R. China

The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.

关键词： Jump systems exponential stability Average dwell time Markov process.

exponential stability of Uncertain T-S Fuzzy Switched Systems with Time Delay

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International Journal of Automation and computing 2013年第1期10卷 32-38页

作者： Fatima Ahmida El Houssaine Tissir Department of Physics Faculty of Sciences

This paper discusses the delay-dependent exponential stability of a class of uncertain T-S fuzzy switched systems with time delay. The method is based on Lyapunov stability theorem and free weighting matrices approach... 详细信息

关键词： Delay dependent stability exponential stability linear matrix inequalities (LMIs) T-S fuzzy switched systems uncertainty

exponential stability Analysis of Cohen-Grossberg Neural Networks with Time-varying Delays

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Acta Mathematicae Applicatae Sinica 2012年第1期28卷 181-192页

作者： Yi-min MENG Li-hong HUANG Zhao-hui YUAN College of Mathematics and Econometrics Hunan UniversityChangshaHunan 410082China

In this paper, we study Cohen-Grossberg neural networks （CGNN） with time-varying delay. Based on Halanay inequality and continuation theorem of the coincidence degree, we obtain some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of periodic solution. Our results complement previously known results.

关键词： neural network exponential stability periodic solution delay

exponential stability and periodic solution for fuzzy BAM Neural networks with time varying delays

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Applied Mathematics(A Journal of Chinese Universities) 2009年第2期24卷 157-166页

作者： XIANG Hong-jun WANG Jin-hua Department of Mathematics, Xiangnan University, Chenzhou 423000, China Department of Mathematics Xiangnan University Chenzhou China

In this paper, a class of fuzzy BAM neural networks with time varying delays is discussed. By using the properties of M-matrix, Linear Matrix Inequality（LMI） approach and general Lyapunov-Krasovskii functional, some new sufficient conditions are derived to ensure the existence of periodic solutions and the global exponential stability of the fuzzy BAM neural networks with time varying delays. These results have important significance in the design of global exponential stable BAM networks with delays. Moreover, an example is given to illustrate that the conditions of the results in the paper are feasible.

关键词： fuzzy BAM neural network periodic solution exponential stability linear matrix inequality(LMI) Lyapunov-Krasovskii functional

exponential stability FOR NONLINEAR HYBRID STOCHASTIC PANTOGRAPH EQUATIONS AND NUMERICAL APPROXIMATION

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Acta Mathematica Scientia 2014年第4期34卷 1254-1270页

作者：周少波薛明皋 School of Mathematics and Statistics Huazhong University of Science and Technology School of Management Huazhong University of Science and Technology

The paper develops exponential stability of the analytic solution and convergence in probability of the numerical method for highly nonlinear hybrid stochastic pantograph equation. The classical linear growth condition is replaced by polynomial growth conditions, under which there exists a unique global solution and the solution is almost surely exponentially stable. On the basis of a series of lemmas, the paper establishes a new criterion on convergence in probability of the Euler-Maruyama approximate solution. The criterion is very general so that many highly nonlinear stochastic pantograph equations can obey these conditions. A highly nonlinear example is provided to illustrate the main theory.

关键词： stochastic pantograph equation hybrid system polynomial growth conditions exponential stability convergence in probability