In this paper, the coupling function of the complex dynamical networks was generalized, and the conditions for the stability of synchronization were given. We illustrate the impact of coupling function on the synchron...In this paper, the coupling function of the complex dynamical networks was generalized, and the conditions for the stability of synchronization were given. We illustrate the impact of coupling function on the synchronization of complex dynamical networks, that is, the coupling strength can not assure the stability of synchronization when the coupling function is linear. However we can modulate coupling function to achieve stability of synchronization without changing coupling strength.展开更多
In this paper, by using both the linear stability analysis and Lyapunov function approach, some conditions for stabilizing synchronization behavior in a discrete-time complex dynamical network were derived. These cond...In this paper, by using both the linear stability analysis and Lyapunov function approach, some conditions for stabilizing synchronization behavior in a discrete-time complex dynamical network were derived. These conditions were determined by the coupling strength and the eigenvalues of coupling configuration matrix. Furthermore, some explicit results were obtained when the coupling map between the nodes is equal to the dynamics function of the network, which implies that the product of the coupling strength and the eigenvalues is bounded.展开更多
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often ...Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance. Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly gains increasing attention in various fields of science and engineering. Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states. The obtained criteria in this paper encompass the established results in the literature as special cases. Some examples are given to illustrate the theoretical results.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
In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous...In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous-time networks with time-varying delay. Based on the stochastic Lyapunov stability theory, Ito＇s differential rule and the linear matrix inequality （LMI） optimization technique, several delay-dependent synchronous criteria are established, which guarantee the asymptotical mean-square synchronization of drive networks and response networks with stochastic disturbances. The criteria are expressed in terms of LMI, which can be easily solved using the Matlab LMI Control Toolbox. Finally, two examples show the effectiveness and feasibility of the proposed synchronous conditions.展开更多
In this paper, the H∞ synchronization is intensively investigated for general delayed complex dynamical networks. The network under consideration contains unknown but bounded nonlinear coupling functions, time-varyin...In this paper, the H∞ synchronization is intensively investigated for general delayed complex dynamical networks. The network under consideration contains unknown but bounded nonlinear coupling functions, time-varying delay, external distur- bances, and lt6-type stochastic disturbances, which is a zero-mean real scalar Wiener process. Based on the stochastic Lyapunov stability theory, Ito＇s differential rule, and linear matrix inequality （LMI） optimization technique, some delay-dependent H∞ synchro- nization schemes are established, which guarantee robust stochas- tically mean square asymptotically synchronization for drive net- work and noise-perturbed response network as well as achieving a prescribed stochastic robust H∞ performance level. Finally, de- tailed and satisfactory numerical results have validated the feasi- bility and the correctness of the proposed techniques.展开更多
This paper concerned with the quantized synchronization analysis problem. The scope of state vectors of dynamic systems, based on the matrix measure, is estimated. By using the general intermittent control, some simpl...This paper concerned with the quantized synchronization analysis problem. The scope of state vectors of dynamic systems, based on the matrix measure, is estimated. By using the general intermittent control, some simple yet generic criteria are derived ensuring the exponential stability of dynamic systems. Then, both the general intermittent networked controller and the quantized parameters can be designed, which guarantee that the nodes of the complex network are synchronized. Finally, simulation examples are given to illustrate the effectiveness and feasibility of the proposed method.展开更多
Recently, much work has been devoted to the study of a large-scale complex system described by a network or a graph with complex topology, whose nodes are the elements of the system and whose edges represent the inter...Recently, much work has been devoted to the study of a large-scale complex system described by a network or a graph with complex topology, whose nodes are the elements of the system and whose edges represent the interactions among them. On the other hand, realistic modelling of many large networks with nonlocal interaction inevitably requires connection delays to be taken into account, since they naturally arise as a consequence of finite information transmission and processing speeds among the units. This paper gives the sufficient conditions guaranteeing the local and global synchronization stability of the complex connected networks by using Lyapunov functional.展开更多
The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the...The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.展开更多
This paper further investigates cluster synchronization in a complex dynamical network with two-cluster.Each cluster contains a number of identical dynamical systems,however,the sub- systems composing the two clusters...This paper further investigates cluster synchronization in a complex dynamical network with two-cluster.Each cluster contains a number of identical dynamical systems,however,the sub- systems composing the two clusters can be different,i.e.,the individual dynamical system in one cluster can differ from that in the other cluster.Complete synchronization within each cluster is possible only if each node from one cluster receives the same input from nodes in other cluster.In this case,the stability condition of one-cluster synchronization is known to contain two terms:the first accounts for the contribution of the inner-cluster coupling structure while the second is simply an extra linear term,which can be deduced by the'same-input'condition.Applying the connection graph stability method,the authors obtain an upper bound of input strength for one cluster if the first account is known,by which the synchronizability of cluster can be scaled.For different clusters,there are different upper bound of input strength by virtue of different dynamics and the corresponding cluster structure.Moreover,two illustrative examples are presented and the numerical simulations coincide with the theoretical analysis.展开更多
Based on the nonlinear measure about /-norm,a novel and effective approach is applied to estimate the scope of state vectors of dynamic systems.By the general intermittent control,some simple yet generic criteria are ...Based on the nonlinear measure about /-norm,a novel and effective approach is applied to estimate the scope of state vectors of dynamic systems.By the general intermittent control,some simple yet generic criteria are derived ensuring the exponential stability of dynamic systems.The numerical simulations,whose theoretical results are applied to robust synchronization of complex networks,demonstrate the effectiveness and feasibility of the proposed technique.展开更多
DQ impedance-based method has been widely used to study the stability of three-phase converter systems.As the dq impedance model of each converter depends on its local dq reference frame,the dq impedance modeling of c...DQ impedance-based method has been widely used to study the stability of three-phase converter systems.As the dq impedance model of each converter depends on its local dq reference frame,the dq impedance modeling of complex converter networks gets complicated.Because the reference frames of different converters might not fully align,depending on the structure.Thus,in order to find an accurate impedance model of a complex network for stability analysis,converting the impedances of different converters into a common reference frame is required.This paper presents a comprehensive investigation on the transformation of dq impedances to a common reference frame in complex converter networks.Four different methods are introduced and analyzed in a systematic way.Moreover,a rigorous comparison among these approaches is carried out,where the method with the simplest transformation procedure is finally suggested for the modeling of complex converter networks.The performed analysis is verified by injecting two independent small-signal perturbations into the d and the q axis,and doing a point-by-point impedance measurement.展开更多
In the past few years, the discovery of small-world and scale-free properties of many natural and artificial complex networks has stimulated increasing interest in further studying the underlying organizing principles...In the past few years, the discovery of small-world and scale-free properties of many natural and artificial complex networks has stimulated increasing interest in further studying the underlying organizing principles of various complex networks. This has led to significant advances in understanding the relationship between the topology and the dynamics of such complex networks. This paper reviews some recent research works on the synchronization phenomenon in various dynamical networks with small-world and scale-free connections.展开更多
To understand the functional behaviors of systems built on networks,it is essential to determine the uncertain topology of these networks.Traditional synchronization-based topology identification methods generally con...To understand the functional behaviors of systems built on networks,it is essential to determine the uncertain topology of these networks.Traditional synchronization-based topology identification methods generally converge asymptotically or exponentially,resulting in their inability to give timely identification results.The finite-time stability theory is adopted in this paper with the aim of addressing the problem of fast identification of uncertain topology in networks.A novel finite-time topology observer is proposed to achieve finite-time topology identification and synchronization of general complex dynamical networks with time delay and second-order dynamical networks with time delay and nonlinear coupling.In addition,the proposed finite-time identification method is applied to power grids to address the problem of fast detection of line outages.Finally,2 numerical experiments are provided to demonstrate the effectiveness and rapidity of the proposed finite-time identification method.展开更多
基金Project supported by National Natural Science Foundation of China (Grant No .10471087) ,and Science Foundation of Shang-hai Municipal Commission of Education (Grant No .03AK33)
文摘In this paper, the coupling function of the complex dynamical networks was generalized, and the conditions for the stability of synchronization were given. We illustrate the impact of coupling function on the synchronization of complex dynamical networks, that is, the coupling strength can not assure the stability of synchronization when the coupling function is linear. However we can modulate coupling function to achieve stability of synchronization without changing coupling strength.
基金Project supported by the National Natural Science Foundation of China （Grant No.10471087）, and Science Foundation of Shanghai Municipal Commission of Education （Grant No.03AK33）
文摘In this paper, by using both the linear stability analysis and Lyapunov function approach, some conditions for stabilizing synchronization behavior in a discrete-time complex dynamical network were derived. These conditions were determined by the coupling strength and the eigenvalues of coupling configuration matrix. Furthermore, some explicit results were obtained when the coupling map between the nodes is equal to the dynamics function of the network, which implies that the product of the coupling strength and the eigenvalues is bounded.
基金supported by National Natural Science Foundation of China under Nos. 10702023 and 10832006China Post-doctoral Special Science Foundation No. 200801020+1 种基金the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant No. 2007110020110supported in part by the Project of Knowledge Innovation Program (PKIP) of Chinese Academy of Sciences
文摘Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance. Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly gains increasing attention in various fields of science and engineering. Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states. The obtained criteria in this paper encompass the established results in the literature as special cases. Some examples are given to illustrate the theoretical results.
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.
基金supported by the National Natural Science Foundation of China (Grant No. 60904060)the Open Foundation of Hubei Province Key Laboratory of Systems Science in Metallurgical Process,China (Grant No. C201010)
文摘In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous-time networks with time-varying delay. Based on the stochastic Lyapunov stability theory, Ito＇s differential rule and the linear matrix inequality （LMI） optimization technique, several delay-dependent synchronous criteria are established, which guarantee the asymptotical mean-square synchronization of drive networks and response networks with stochastic disturbances. The criteria are expressed in terms of LMI, which can be easily solved using the Matlab LMI Control Toolbox. Finally, two examples show the effectiveness and feasibility of the proposed synchronous conditions.
基金Supported by the National Natural Science Foundation of China(6090406061104127)
文摘In this paper, the H∞ synchronization is intensively investigated for general delayed complex dynamical networks. The network under consideration contains unknown but bounded nonlinear coupling functions, time-varying delay, external distur- bances, and lt6-type stochastic disturbances, which is a zero-mean real scalar Wiener process. Based on the stochastic Lyapunov stability theory, Ito＇s differential rule, and linear matrix inequality （LMI） optimization technique, some delay-dependent H∞ synchro- nization schemes are established, which guarantee robust stochas- tically mean square asymptotically synchronization for drive net- work and noise-perturbed response network as well as achieving a prescribed stochastic robust H∞ performance level. Finally, de- tailed and satisfactory numerical results have validated the feasi- bility and the correctness of the proposed techniques.
文摘This paper concerned with the quantized synchronization analysis problem. The scope of state vectors of dynamic systems, based on the matrix measure, is estimated. By using the general intermittent control, some simple yet generic criteria are derived ensuring the exponential stability of dynamic systems. Then, both the general intermittent networked controller and the quantized parameters can be designed, which guarantee that the nodes of the complex network are synchronized. Finally, simulation examples are given to illustrate the effectiveness and feasibility of the proposed method.
文摘Recently, much work has been devoted to the study of a large-scale complex system described by a network or a graph with complex topology, whose nodes are the elements of the system and whose edges represent the interactions among them. On the other hand, realistic modelling of many large networks with nonlocal interaction inevitably requires connection delays to be taken into account, since they naturally arise as a consequence of finite information transmission and processing speeds among the units. This paper gives the sufficient conditions guaranteeing the local and global synchronization stability of the complex connected networks by using Lyapunov functional.
基金supported by National Natural Science Foundation of China(No.61273008)Science Research Project of Liaoning Provicial Education Department(No.L2012208)Science Foundation of Ministry of Housing and Urban-Rural Development(No.2013-K5-2)
文摘The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.
基金the National Natural Science Foundation of China under Grant Nos.70771084 and 60574045the National Basic Research Program of China under Grant No.2007CB310805
文摘This paper further investigates cluster synchronization in a complex dynamical network with two-cluster.Each cluster contains a number of identical dynamical systems,however,the sub- systems composing the two clusters can be different,i.e.,the individual dynamical system in one cluster can differ from that in the other cluster.Complete synchronization within each cluster is possible only if each node from one cluster receives the same input from nodes in other cluster.In this case,the stability condition of one-cluster synchronization is known to contain two terms:the first accounts for the contribution of the inner-cluster coupling structure while the second is simply an extra linear term,which can be deduced by the'same-input'condition.Applying the connection graph stability method,the authors obtain an upper bound of input strength for one cluster if the first account is known,by which the synchronizability of cluster can be scaled.For different clusters,there are different upper bound of input strength by virtue of different dynamics and the corresponding cluster structure.Moreover,two illustrative examples are presented and the numerical simulations coincide with the theoretical analysis.
基金supported by Project of Shandong Province Higher Educational Science and Technology Program(J13LI02)Research Fund Project of Heze University under Grant:XY10KZ01
文摘Based on the nonlinear measure about /-norm,a novel and effective approach is applied to estimate the scope of state vectors of dynamic systems.By the general intermittent control,some simple yet generic criteria are derived ensuring the exponential stability of dynamic systems.The numerical simulations,whose theoretical results are applied to robust synchronization of complex networks,demonstrate the effectiveness and feasibility of the proposed technique.
基金The support of the first and fourth authors is given by National Key R&D Program of China,2018YFB0905200.The support for the second and third authors is coming from BIRD171227/17 project of the University of Padova.
文摘DQ impedance-based method has been widely used to study the stability of three-phase converter systems.As the dq impedance model of each converter depends on its local dq reference frame,the dq impedance modeling of complex converter networks gets complicated.Because the reference frames of different converters might not fully align,depending on the structure.Thus,in order to find an accurate impedance model of a complex network for stability analysis,converting the impedances of different converters into a common reference frame is required.This paper presents a comprehensive investigation on the transformation of dq impedances to a common reference frame in complex converter networks.Four different methods are introduced and analyzed in a systematic way.Moreover,a rigorous comparison among these approaches is carried out,where the method with the simplest transformation procedure is finally suggested for the modeling of complex converter networks.The performed analysis is verified by injecting two independent small-signal perturbations into the d and the q axis,and doing a point-by-point impedance measurement.
基金This research is supported by the National Science Fund for Distinguished Young Scholars(60225013)and National Natural Science Foundation of China through the grant numbers 60174005 and 70271072,and the Hong Kong Research Grants Council under the CERG gr
文摘In the past few years, the discovery of small-world and scale-free properties of many natural and artificial complex networks has stimulated increasing interest in further studying the underlying organizing principles of various complex networks. This has led to significant advances in understanding the relationship between the topology and the dynamics of such complex networks. This paper reviews some recent research works on the synchronization phenomenon in various dynamical networks with small-world and scale-free connections.
基金supported by the National Natural Science Foundation of China(61973133 and 62373162)Natural Science Foundation of Hubei Province of China(2022CFA052).
文摘To understand the functional behaviors of systems built on networks,it is essential to determine the uncertain topology of these networks.Traditional synchronization-based topology identification methods generally converge asymptotically or exponentially,resulting in their inability to give timely identification results.The finite-time stability theory is adopted in this paper with the aim of addressing the problem of fast identification of uncertain topology in networks.A novel finite-time topology observer is proposed to achieve finite-time topology identification and synchronization of general complex dynamical networks with time delay and second-order dynamical networks with time delay and nonlinear coupling.In addition,the proposed finite-time identification method is applied to power grids to address the problem of fast detection of line outages.Finally,2 numerical experiments are provided to demonstrate the effectiveness and rapidity of the proposed finite-time identification method.
