We deal with the problem of pinning sampled-data synchronization for a complex network with probabilistic time-varying coupling delay. The sampling period considered here is assumed to be less than a given bound. With...We deal with the problem of pinning sampled-data synchronization for a complex network with probabilistic time-varying coupling delay. The sampling period considered here is assumed to be less than a given bound. Without using the Kronecker product, a new synchronization error system is constructed by using the property of the random variable and input delay approach. Based on the Lyapunov theory, a delay-dependent pinning sampled-data synchronization criterion is derived in terms of linear matrix inequalities （LMIs） that can be solved effectively by using MATLAB LMI toolbox. Numerical examples are provided to demonstrate the effectiveness of the proposed scheme.展开更多
In the recent research of network sampling, some sampling concepts are misunderstood, and the variance of subnets is not taken into account. We propose the correct definition of the sample and sampling rate in network...In the recent research of network sampling, some sampling concepts are misunderstood, and the variance of subnets is not taken into account. We propose the correct definition of the sample and sampling rate in network sampling, as well as the formula for calculating the variance of subnets. Then, three commonly used sampling strategies are applied to databases of the connecting nearest-neighbor（CNN） model, random network and small-world network to explore the variance in network sampling. As proved by the results, snowball sampling obtains the most variance of subnets, but does well in capturing the network structure. The variance of networks sampled by the hub and random strategy are much smaller. The hub strategy performs well in reflecting the property of the whole network, while random sampling obtains more accurate results in evaluating clustering coefficient.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
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61203049 and 61303020)the Natural Science Foundation of Shanxi Province of China(Grant No.2013021018-3)the Doctoral Startup Foundation of Taiyuan University of Science and Technology,China(Grant No.20112010)
文摘We deal with the problem of pinning sampled-data synchronization for a complex network with probabilistic time-varying coupling delay. The sampling period considered here is assumed to be less than a given bound. Without using the Kronecker product, a new synchronization error system is constructed by using the property of the random variable and input delay approach. Based on the Lyapunov theory, a delay-dependent pinning sampled-data synchronization criterion is derived in terms of linear matrix inequalities （LMIs） that can be solved effectively by using MATLAB LMI toolbox. Numerical examples are provided to demonstrate the effectiveness of the proposed scheme.
基金supported by the Basic Research Fund of Beijing Institute of Technology(20120642008)
文摘In the recent research of network sampling, some sampling concepts are misunderstood, and the variance of subnets is not taken into account. We propose the correct definition of the sample and sampling rate in network sampling, as well as the formula for calculating the variance of subnets. Then, three commonly used sampling strategies are applied to databases of the connecting nearest-neighbor（CNN） model, random network and small-world network to explore the variance in network sampling. As proved by the results, snowball sampling obtains the most variance of subnets, but does well in capturing the network structure. The variance of networks sampled by the hub and random strategy are much smaller. The hub strategy performs well in reflecting the property of the whole network, while random sampling obtains more accurate results in evaluating clustering coefficient.
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.
