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 n...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.展开更多
Based on the Chen chaotic system, a new four-dimensional hyperchaotic Chen system is constructed, and the basic dynamic behaviours of the system were studied, and the generalized synchronization has been observed in t...Based on the Chen chaotic system, a new four-dimensional hyperchaotic Chen system is constructed, and the basic dynamic behaviours of the system were studied, and the generalized synchronization has been observed in the coupled four-dimensional hyperchaotic Chen system with unknown parameters. The Routh Hurwitz theorem is used to derive the conditions of stability of this system. Furthermore based on Lyapunov stability theory, the control laws and adaptive laws of parameters are obtained to make generalized synchronization of the coupled new four-dimensional hyperchaotic Chen systems. Numerical simulation results are presented to illustrate the effectiveness of this method.展开更多
Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme. In this paper, a non-fragile linear feedback control strategy with multipl...Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme. In this paper, a non-fragile linear feedback control strategy with multiplicative controller gain uncertainties is proposed for realizing the mixed-synchronization of Chua＇s circuits connected in a drive-response configuration. In particular, in the mixed-synchronization regime, different state variables of the response system can evolve into complete synchronization, anti-synchronization and even amplitude death simultaneously with the drive variables for an appropriate choice of scaling matrix. Using Lyapunov stability theory, we derive some sufficient criteria for achieving global mixed-synchronization. It is shown that the desired non-fragile state feedback controller can be constructed by solving a set of linear matrix inequalities （LMIs）. Numerical simulations are also provided to demonstrate the effectiveness of the proposed control approach.展开更多
This paper further investigates the synchronization problem of a new chaotic system with known or unknown system parameters. Based on the Lyapunov stability theory,a novel adaptive control law is derived for the synch...This paper further investigates the synchronization problem of a new chaotic system with known or unknown system parameters. Based on the Lyapunov stability theory,a novel adaptive control law is derived for the synchronization of a new chaotic system with known or unknown system parameters.Theoretical analysis and numerical simulations showthe effectiveness and feasibility of the proposed schemes.展开更多
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...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.展开更多
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 s...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.展开更多
A guidance policy for controller performance enhancement utilizing mobile sensor-actuator networks （MSANs） is proposed for a class of distributed parameter systems （DPSs）, which are governed by diffusion partial d...A guidance policy for controller performance enhancement utilizing mobile sensor-actuator networks （MSANs） is proposed for a class of distributed parameter systems （DPSs）, which are governed by diffusion partial differential equations （PDEs） with time-dependent spatial domains. Several sufficient conditions for controller performance enhancement are presented. First, the infinite dimensional operator theory is used to derive an abstract evolution equation of the systems under some rational assumptions on the operators, and a static output feedback controller is designed to control the spatial process. Then, based on Lyapunov stability arguments, guidance policies for collocated and non-collocated MSANs are provided to enhance the performance of the proposed controller, which show that the time-dependent characteristic of the spatial domains can significantly affect the design of the mobile scheme. Finally, a simulation example illustrates the effectiveness of the proposed policy.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
A sliding mode control approach is proposed to implement the synchronization of the chain tree network. The doublescroll circuit chaos systems are treated as nodes and the network is constructed with the state variabl...A sliding mode control approach is proposed to implement the synchronization of the chain tree network. The doublescroll circuit chaos systems are treated as nodes and the network is constructed with the state variable coupling. By selecting a switching sliding surface, the chaos synchronization of the network is achieved with one control input only. The stability analysis and the numerical simulations demonstrate that the complete synchronization in a chain network can be realized for all nodes.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
This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between, within, and across layers. Based on the Lyapunov stability ...This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between, within, and across layers. Based on the Lyapunov stability method, we prove theoretically that the duplex network can achieve intra-layer synchronization under some appropriate conditions, and give the thresholds of coupling strength within layers for different types of inner coupling matrices across layers. Interestingly,for a certain class of coupling matrices across layers, it needs larger coupling strength within layers to ensure the intra-layer synchronization when the coupling strength across layers become larger, intuitively opposing the fact that the intra-layer synchronization is seemly independent of the coupling strength across layers. Finally, numerical simulations further verify the theoretical results.展开更多
In this paper, a fuzzy operator of max-product is defined at first, and the fuzzy bi-directional associative memory (FBAM) based on the fuzzy operator of max-product is given. Then the properties and the Lyapunov stab...In this paper, a fuzzy operator of max-product is defined at first, and the fuzzy bi-directional associative memory (FBAM) based on the fuzzy operator of max-product is given. Then the properties and the Lyapunov stability of equilibriums of the networks are studied.展开更多
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 ...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.展开更多
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 connectio...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.展开更多
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. T...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.展开更多
We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional（2D） systems.The mathematical model of the discrete-time 2D system is established upon the well-known Roesser model,and...We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional（2D） systems.The 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 domain.The stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the Lyapunov stability theory.In the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques.Moreover,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,numerical examples are given to demonstrate the effectiveness of the obtained results.展开更多
This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties....This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties. The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties. By constructing an appropriate Lyapunov-Krasvskii functional, a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality. From the derived criterion, the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically. A simulation example is given to illustrate the effectiveness of the proposed design method,展开更多
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 projecti...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.展开更多
With system parameters falling into a certain area, power system with excitation limits experiences complicated chaotic oscillations which threaten the secure and stable operation of power system. In this paper, to co...With system parameters falling into a certain area, power system with excitation limits experiences complicated chaotic oscillations which threaten the secure and stable operation of power system. In this paper, to control these unwanted chaotic oscillations, a straightforward adaptive chaos controller based on Lyapunov asymptotical stability theory is designed. Since the presented controller does not need to change the controlled system structure and not to use any information of system except the system state variables, the designed controller is simple and desirable. Simulation results show that the proposed control law is very effective. This work is helpful to maintain the power system＇s security operation.展开更多
In this article, the permanence and persistence for thrce classes time varying Lotka-Volterra ecological system are investigated by using Lyapunov stability analysis and constrncting the compact set of attraction. Som...In this article, the permanence and persistence for thrce classes time varying Lotka-Volterra ecological system are investigated by using Lyapunov stability analysis and constrncting the compact set of attraction. Some examples are given to illustrate the theorems.展开更多
基金Project supported by the Natural Science Foundation of Liaoning Province,China(Grant No.20082147)the Innovative Team Program of Liaoning Educational Committee,China(Grant No.2008T108)
文摘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.
文摘Based on the Chen chaotic system, a new four-dimensional hyperchaotic Chen system is constructed, and the basic dynamic behaviours of the system were studied, and the generalized synchronization has been observed in the coupled four-dimensional hyperchaotic Chen system with unknown parameters. The Routh Hurwitz theorem is used to derive the conditions of stability of this system. Furthermore based on Lyapunov stability theory, the control laws and adaptive laws of parameters are obtained to make generalized synchronization of the coupled new four-dimensional hyperchaotic Chen systems. Numerical simulation results are presented to illustrate the effectiveness of this method.
基金Project supported by the Foundation for Distinguished Young Talents in Higher Education of Guangdong Province of China(Grant No. LYM10074)the Natural Science Foundation of Guangdong Province,China (Grant No. 9451042001004076)
文摘Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme. In this paper, a non-fragile linear feedback control strategy with multiplicative controller gain uncertainties is proposed for realizing the mixed-synchronization of Chua＇s circuits connected in a drive-response configuration. In particular, in the mixed-synchronization regime, different state variables of the response system can evolve into complete synchronization, anti-synchronization and even amplitude death simultaneously with the drive variables for an appropriate choice of scaling matrix. Using Lyapunov stability theory, we derive some sufficient criteria for achieving global mixed-synchronization. It is shown that the desired non-fragile state feedback controller can be constructed by solving a set of linear matrix inequalities （LMIs）. Numerical simulations are also provided to demonstrate the effectiveness of the proposed control approach.
文摘This paper further investigates the synchronization problem of a new chaotic system with known or unknown system parameters. Based on the Lyapunov stability theory,a novel adaptive control law is derived for the synchronization of a new chaotic system with known or unknown system parameters.Theoretical analysis and numerical simulations showthe effectiveness and feasibility of the proposed schemes.
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61174021 and 61473136)
文摘A guidance policy for controller performance enhancement utilizing mobile sensor-actuator networks （MSANs） is proposed for a class of distributed parameter systems （DPSs）, which are governed by diffusion partial differential equations （PDEs） with time-dependent spatial domains. Several sufficient conditions for controller performance enhancement are presented. First, the infinite dimensional operator theory is used to derive an abstract evolution equation of the systems under some rational assumptions on the operators, and a static output feedback controller is designed to control the spatial process. Then, based on Lyapunov stability arguments, guidance policies for collocated and non-collocated MSANs are provided to enhance the performance of the proposed controller, which show that the time-dependent characteristic of the spatial domains can significantly affect the design of the mobile scheme. Finally, a simulation example illustrates the effectiveness of the proposed policy.
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.
基金Project supported by the State Key Program of the National Natural Science Foundation of China(Grant No.11232009)the Shanghai Leading Academic Discipline Project,China(Grant No.S30106)
文摘A sliding mode control approach is proposed to implement the synchronization of the chain tree network. The doublescroll circuit chaos systems are treated as nodes and the network is constructed with the state variable coupling. By selecting a switching sliding surface, the chaos synchronization of the network is achieved with one control input only. The stability analysis and the numerical simulations demonstrate that the complete synchronization in a chain network can be realized for all nodes.
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.
基金Project supported in part by the National Natural Science Foundation of China(Grant Nos.61573004 and 11501221)the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University(Grant No.ZQN-YX301)+1 种基金the Program for New Century Excellent Talents in Fujian Province University in 2016the Project of Education and Scientific Research for Middle and Young Teachers in Fujian Province,China(Grant Nos.JAT170027 and JA15030)
文摘This paper explores the intra-layer synchronization in duplex networks with different topologies within layers and different inner coupling patterns between, within, and across layers. Based on the Lyapunov stability method, we prove theoretically that the duplex network can achieve intra-layer synchronization under some appropriate conditions, and give the thresholds of coupling strength within layers for different types of inner coupling matrices across layers. Interestingly,for a certain class of coupling matrices across layers, it needs larger coupling strength within layers to ensure the intra-layer synchronization when the coupling strength across layers become larger, intuitively opposing the fact that the intra-layer synchronization is seemly independent of the coupling strength across layers. Finally, numerical simulations further verify the theoretical results.
文摘In this paper, a fuzzy operator of max-product is defined at first, and the fuzzy bi-directional associative memory (FBAM) based on the fuzzy operator of max-product is given. Then the properties and the Lyapunov stability of equilibriums of the networks are studied.
基金supported by the National Natural Science Foundation of China (Grant Nos 70571030 and 90610031)the Advanced Talent Foundation of Jiangsu University of China (Grant No 07JDG054)
文摘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.
基金Project supported by the Natural Science Foundation of Liaoning Province,China(Grant No.20082147)the Innovative Team Program of Liaoning Educational Committee,China(Grant No.2008T108)
文摘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.
基金supported by the Industrial Technology Research and Development Special Project of Jilin Province,China(Grant No.2013C46)the Natural Science Foundation of Jilin Province,China(Grant No.20101510)
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61104010)
文摘We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional（2D） systems.The 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 domain.The stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the Lyapunov stability theory.In the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques.Moreover,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,numerical examples are given to demonstrate the effectiveness of the obtained results.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61104138)the Guangdong Natural Science Foundation,China (Grant No. S2011040001704)the Foundation for Distinguished Young Talents in Higher Education of Guangdong,China (Grant No. LYM10074)
文摘This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties. The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties. By constructing an appropriate Lyapunov-Krasvskii functional, a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality. From the derived criterion, the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically. A simulation example is given to illustrate the effectiveness of the proposed design method,
文摘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.
基金Project supported by the National Natural Science Foundation of China （Grant No 70571017）.
文摘With system parameters falling into a certain area, power system with excitation limits experiences complicated chaotic oscillations which threaten the secure and stable operation of power system. In this paper, to control these unwanted chaotic oscillations, a straightforward adaptive chaos controller based on Lyapunov asymptotical stability theory is designed. Since the presented controller does not need to change the controlled system structure and not to use any information of system except the system state variables, the designed controller is simple and desirable. Simulation results show that the proposed control law is very effective. This work is helpful to maintain the power system＇s security operation.
文摘In this article, the permanence and persistence for thrce classes time varying Lotka-Volterra ecological system are investigated by using Lyapunov stability analysis and constrncting the compact set of attraction. Some examples are given to illustrate the theorems.
