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New results on the robust stability analysis of neural networks with discrete and distributed time delays

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Journal of Systems Engineering and Electronics 2008年第3期19卷 592-597页

作者： Su Weiwei Chen Yiming Coll. of Science Yanshan Univ. Qinhuangdao 066004 P. R. China

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.

关键词： neural networks delay-dependent robust stability lyapunov stability theory linear matrix inequality(LMI) distributed delay norm-bounded uncertainties.

Chaotic synchronization in Bose Einstein condensate of moving optical lattices via linear coupling

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Chinese Physics B 2015年第11期24卷 151-156页

作者：张志颖冯秀琴姚治海贾洪洋 School of Science Changchun University of Science and Technology

A systematic study of the chaotic synchronization of Bose-Einstein condensed body is performed using linear cou- pling method based on lyapunov stability theory, Sylvester＇s criterion, and Gerschgorin disc theorem. The chaotic synchro- nization of Bose-Einstein condensed body in moving optical lattices is realized by linear coupling. The relationship be- tween the synchronization time and coupling coefficient is obtained. Both the single-variable coupling and double-variable coupling are effective. The results of numerical calculation prove that the chaotic synchronization of double-variable cou- pling is faster than that of single-variable coupling and small coupling coefficient can achieve the chaotic synchronization. Weak noise has little influence on synchronization effect, so the linear coupling technology is suitable for the chaotic synchronization of Bose-Einstein condensate.

关键词： Bose-Einstein condensate linear coupling chaos synchronization lyapunov stability theory

Projective synchronization of spatiotemporal chaos in a weighted complex network

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Chinese Physics B 2010年第8期19卷 171-176页

作者：吕翎柴元栾玲 College of Physics and Electronic Technology Liaoning Normal University Physical Science and Technology Institute Dalian University

Projective synchronization of a weighted complex network is studied in which nodes are spatiotemporal chaos systems and all nodes are coupled not with the nonlinear terms of the system but through a weighted connection. The range of the linear coefficient matrix of separated configuration, when the synchronization is implemented, is determined according to lyapunov stability theory. It is found that projective synchronization can be realized for unidirectional star-connection even if the coupling strength between the nodes is a given arbitrary weight value. The Gray-Scott models having spatiotemporal Chaos behaviours are taken as nodes in the weighted complex network, and simulation results of spatiotemporal synchronization show the effectiveness of the method.

关键词： weighted network spatiotemporal chaos projective synchronization lyapunov stability theory

Adaptive control and synchronization of an uncertain new hyperchaotic Lorenz system

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Chinese Physics B 2008年第7期17卷 2412-2419页

作者：蔡国梁郑松田立新 Nonlinear Scientific Research Center Jiangsu University

This paper is involved with the adaptive control and synchronization problems for an uncertain new hyperchaotic Lorenz system. Based on the lyapunov stability theory, the adaptive control law is derived such that the trajectory of hyperchaotic Lorenz system with unknown parameters can be globally stabilized to an unstable equilibrium point of the uncontrolled system. Furthermore, an adaptive control approach is presented to the synchronizations between two identical hyperchaotic systems, particularly between two different uncertain hyperchaotic systems. Numerical simulations show the effectiveness of the presented method.

关键词： hyperchaotic Lorenz system control synchronization lyapunov stability theory

Adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions

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Chinese Physics B 2012年第12期21卷 141-152页

作者：戴浩贾立新张彦斌 State Key Laboratory of Electrical Insulation and Power Equipment School of Electrical EngineeringXi'an Jiaotong University

The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on lyapunov stability theory and Barbalat＇s lemma, generalized matrix projective lag synchronization criteria are derived by using the adaptive control method. Furthermore, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. In addition, numerical simulation results are presented to illustrate the effectiveness of this method, showing that the synchronization speed is sensitively influenced by the adaptive law strength, the network size, and the network topological structure.

关键词： complex networks generalized matrix projective lag synchronization adaptive control lyapunov stability theory

stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems

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Chinese Physics B 2013年第3期22卷 79-84页

作者：王佳会国涛解相朋 School of Mechanical and Vehicular Engineering Beijing Institute of Technology School of Information Science and Engineering Northeastern University

We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional（2D） *** mathematical model of the discrete-time 2D system is established upon the well-known Roesser model,and the uncertainty phenomenon,which appears typically in practical environments,is modeled by a convex bounded（polytope type） uncertain *** stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the lyapunov stability *** the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed ***,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical ***,numerical examples are given to demonstrate the effectiveness of the obtained results.

关键词： uncertain two-dimensional systems Roesser model lyapunov stability theory control synthesis

Generalized chaos synchronization of a weighted complex network with different nodes

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Chinese Physics B 2010年第8期19卷 177-183页

作者：吕翎李钢郭丽孟乐邹家蕊杨明 College of Physics and Electronic Technology Liaoning Normal University

This paper proposes a method of realizing generalized chaos synchronization of a weighted complex network with different nodes. Chaotic systems with diverse structures are taken as the nodes of the complex dynamical network, the nonlinear terms of the systems are taken as coupling functions, and the relations among the nodes are built through weighted connections. The structure of the coupling functions between the connected nodes is obtained based on lyapunov stability theory. A complex network with nodes of Lorenz system, Coullet system, RSssler system and the New system is taken as an example for simulation study and the results show that generalized chaos synchronization exists in the whole weighted complex network with different nodes when the coupling strength among the nodes is given with any weight value. The method can be used in realizing generalized chaos synchronization of a weighted complex network with different nodes. Furthermore, both the weight value of the coupling strength among the nodes and the number of the nodes have no effect on the stability of synchronization in the whole complex network.

关键词： chaos synchronization weighted network diverse structure lyapunov stability theory

A new four-dimensional hyperchaotic Lorenz system and its adaptive control

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Chinese Physics B 2011年第1期20卷 229-237页

作者：司刚全曹晖张彦斌 State Key Laboratory of Electrical Insulation and Power Equipment School of Electrical EngineeringXi'an Jiaotong University

Based on the Lorenz chaotic system, this paper constructs a new four-dimensional hyperchaotic Lorenz system, and studies the basic dynamic behaviours of the system. The Routh-Hurwitz theorem is applied to derive the stability conditions of the proposed system. Furthermore, based on lyapunov stability theory, an adaptive controller is designed and the new four-dimensional hyperchaotic Lorenz system is controlled at equilibrium point. Numerical simulation results are presented to illustrate the effectiveness of this method.

关键词： hyperchaotic Lorenz system adaptive control lyapunov stability theory

A new three-dimensional chaotic system and its modified generalized projective synchronization

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Chinese Physics B 2011年第4期20卷 139-148页

作者：戴浩贾立新惠萌司刚全 State Key Laboratory of Electrical Insulation and Power Equipment School of Electrical EngineeringXi'an Jiaotong University

Based on the Chen chaotic system, this paper constructs a new three-dimensional chaotic system with higher order nonlinear term and studies the basic dynamic behaviours of the system. The modified generalized projective synchronization has been observed in the coupled new three-dimensional chaotic system with unknown parameters. Furthermore, based on lyapunov stability theory, it obtains the control laws and adaptive laws of parameters to make modified generalized projective synchronization of the coupled new three-dimensional chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.

关键词： chaotic system generalized projective synchronization lyapunov stability theory