In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the a...In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities （LMIs）. Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin＇s formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.展开更多
Synchronization of high-order discrete-time complex networks with undirected topologies is studied and the impacts of time delays are investigated. Firstly,by the state decomposition,synchronization problems are trans...Synchronization of high-order discrete-time complex networks with undirected topologies is studied and the impacts of time delays are investigated. Firstly,by the state decomposition,synchronization problems are transformed into asymptotic stability ones of multiple lower dimensional time-delayed subsystems. Then,linear matrix inequality( LMI) criteria for synchronization are given,which can guarantee the scalability of complex networks since they only include three LMI constraints independent of the number of agents. Moreover,an explicit expression of the synchronization function is presented,which can describe the synchronization behavior of all agents in complex networks. Finally,a numerical example is given to demonstrate the theoretical results,where it is shown that if the gain matrices of synchronization protocols satisfy LMI criteria for synchronization,synchronization can be achieved.展开更多
In this article, the notion of pinning control for directed networks of dynamical systems is introduced, where the nodes could be either single-input single-output （SISO） or multi-input multi-output （MIMO） dynamic...In this article, the notion of pinning control for directed networks of dynamical systems is introduced, where the nodes could be either single-input single-output （SISO） or multi-input multi-output （MIMO） dynamical systems, and could be non-identical and nonlinear in general but will be specified to be identical linear time-invariant （LTI） systems here in the study of network controllability. Both state and structural controllability problems will be discussed, illustrating how the network topology, node-system dynamics, external control inputs and inner dynamical interactions altogether affect the controllability of a general complex network of LTI systems, with necessary and sufficient conditions presented for both SISO and MIMO settings. To that end, the controllability of a special temporally switching directed network of linear time-varying （LTV） node systems will be addressed, leaving some more general networks and challenging issues to the end for research outlook.展开更多
This paper deals with the cluster exponential synchronization of a class ot complex networks wlm nyorm coupm^g and time-varying delay. Through constructing an appropriate Lyapunov-Krasovskii functional and applying th...This paper deals with the cluster exponential synchronization of a class ot complex networks wlm nyorm coupm^g and time-varying delay. Through constructing an appropriate Lyapunov-Krasovskii functional and applying the theory of the Kronecker product of matrices and the linear matrix inequality （LMI） technique, several novel sufficient conditions for cluster exponential synchronization are obtained. These cluster exponential synchronization conditions adopt the bounds of both time delay and its derivative, which are less conservative. Finally, the numerical simulations are performed to show the effectiveness of the theoretical results.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
This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur＇e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small ...This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur＇e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small fraction of the nodes. The pinning control problem is reformulated in the framework of the absolute stability theory. It is shown that the global stability of the controlled network can be reduced to the test of a set of linear matrix inequalities, which in turn guarantee the absolute stability of the corresponding Lur＇e systems whose dimensions are the same as that of a single node. A circle-type criterion in the frequency domain is further presented for checking the stability of the controlled network graphically. Finally, a network of Chua＇s oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results.展开更多
In this paper, the problem of exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and Mode-dependent probabilistic time-varying coupling delays is investigate...In this paper, the problem of exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and Mode-dependent probabilistic time-varying coupling delays is investigated. The sam- pling period is assumed to be time-varying and bounded. The information of probability distribution of the time-varying delay is considered and transformed into parameter matrices of the transferred complex dynamical network model. Based on the condition, the design method of the desired sampled data controller is proposed. By constructing a new Lyapunov functional with triple integral terms, delay-distribution-dependent exponential synchronization criteria are derived in the form of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.展开更多
This paper deals with the issue of synchronization of delayed complex networks. Differing from previous results, the delay interval [0, d（t）] is divided into some variable subintervals by employing a new method of w...This paper deals with the issue of synchronization of delayed complex networks. Differing from previous results, the delay interval [0, d（t）] is divided into some variable subintervals by employing a new method of weighting delays. Thus, new synchronization criteria for complex networks with time-varying delays are derived by applying this weighting-delay method and introducing some free weighting matrices. The obtained results have proved to be less conservative than previous results. The sufficient conditions of asymptotical synchronization are derived in the form of linear matrix inequality, which are easy to verify. Finally, several simulation examples are provided to show the effectiveness of the proposed results.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
The syntheses and structures of eleven novel polymeric transition metal complexes having one dimensional chain structures or three dimensional networks are summarized. They are prepared from the controlled assemblin...The syntheses and structures of eleven novel polymeric transition metal complexes having one dimensional chain structures or three dimensional networks are summarized. They are prepared from the controlled assembling reactions in organic solvents and characterized by X ray diffraction analyses. The spectroscopic or magnetic properties of some complexes are studied.展开更多
文摘In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities （LMIs）. Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin＇s formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61374054,61174067,61263002)the Shaanxi Province Natural Science Foundation Research Projection(Grant No.2013JQ8038)
文摘Synchronization of high-order discrete-time complex networks with undirected topologies is studied and the impacts of time delays are investigated. Firstly,by the state decomposition,synchronization problems are transformed into asymptotic stability ones of multiple lower dimensional time-delayed subsystems. Then,linear matrix inequality( LMI) criteria for synchronization are given,which can guarantee the scalability of complex networks since they only include three LMI constraints independent of the number of agents. Moreover,an explicit expression of the synchronization function is presented,which can describe the synchronization behavior of all agents in complex networks. Finally,a numerical example is given to demonstrate the theoretical results,where it is shown that if the gain matrices of synchronization protocols satisfy LMI criteria for synchronization,synchronization can be achieved.
文摘In this article, the notion of pinning control for directed networks of dynamical systems is introduced, where the nodes could be either single-input single-output （SISO） or multi-input multi-output （MIMO） dynamical systems, and could be non-identical and nonlinear in general but will be specified to be identical linear time-invariant （LTI） systems here in the study of network controllability. Both state and structural controllability problems will be discussed, illustrating how the network topology, node-system dynamics, external control inputs and inner dynamical interactions altogether affect the controllability of a general complex network of LTI systems, with necessary and sufficient conditions presented for both SISO and MIMO settings. To that end, the controllability of a special temporally switching directed network of linear time-varying （LTV） node systems will be addressed, leaving some more general networks and challenging issues to the end for research outlook.
基金supported by the National Natural Science Foundation of China (Grant Nos. 61074073 and 61034005)the Fundamental Research Funds for the Central Universities of China (Grant No. N110504001)the Open Project of the State Key Laboratory of Management and Control for Complex Systems, China (Grant No. 20110107)
文摘This paper deals with the cluster exponential synchronization of a class ot complex networks wlm nyorm coupm^g and time-varying delay. Through constructing an appropriate Lyapunov-Krasovskii functional and applying the theory of the Kronecker product of matrices and the linear matrix inequality （LMI） technique, several novel sufficient conditions for cluster exponential synchronization are obtained. These cluster exponential synchronization conditions adopt the bounds of both time delay and its derivative, which are less conservative. Finally, the numerical simulations are performed to show the effectiveness of the theoretical results.
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Project supported by the Aviation Science Funds (Grant No 20080751019)
文摘This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur＇e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small fraction of the nodes. The pinning control problem is reformulated in the framework of the absolute stability theory. It is shown that the global stability of the controlled network can be reduced to the test of a set of linear matrix inequalities, which in turn guarantee the absolute stability of the corresponding Lur＇e systems whose dimensions are the same as that of a single node. A circle-type criterion in the frequency domain is further presented for checking the stability of the controlled network graphically. Finally, a network of Chua＇s oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results.
基金Project supported by the NBHM Research Project (Grant Nos.2/48(7)/2012/NBHM(R.P.)/R and D II/12669)
文摘In this paper, the problem of exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and Mode-dependent probabilistic time-varying coupling delays is investigated. The sam- pling period is assumed to be time-varying and bounded. The information of probability distribution of the time-varying delay is considered and transformed into parameter matrices of the transferred complex dynamical network model. Based on the condition, the design method of the desired sampled data controller is proposed. By constructing a new Lyapunov functional with triple integral terms, delay-distribution-dependent exponential synchronization criteria are derived in the form of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.
基金supported by the National Natural Science Foundation of China (Grant Nos. 50977008,60774048 and 61034005)the Research Fund for the Doctoral Program of China Higher Education (Grant No. 20070145015)the National High Technology Research and Development Program of China (Grant No. 2009AA04Z127)
文摘This paper deals with the issue of synchronization of delayed complex networks. Differing from previous results, the delay interval [0, d（t）] is divided into some variable subintervals by employing a new method of weighting delays. Thus, new synchronization criteria for complex networks with time-varying delays are derived by applying this weighting-delay method and introducing some free weighting matrices. The obtained results have proved to be less conservative than previous results. The sufficient conditions of asymptotical synchronization are derived in the form of linear matrix inequality, which are easy to verify. Finally, several simulation examples are provided to show the effectiveness of the proposed results.
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The syntheses and structures of eleven novel polymeric transition metal complexes having one dimensional chain structures or three dimensional networks are summarized. They are prepared from the controlled assembling reactions in organic solvents and characterized by X ray diffraction analyses. The spectroscopic or magnetic properties of some complexes are studied.
