Synchronization of Markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time-varying delays

Abstract

The paper investigates the synchronization stability problem for a class of complex dynamical networks with Markovian jumping parameters and mixed time delays. The complex networks consist of m modes and the networks switch from one mode to another according to a Markovian chain with known transition probability. The mixed time delays are composed of discrete and distributed delays, the discrete time delay is assumed to be random and its probability distribution is known a priori. In terms of the probability distribution of the delays, the new type of system model with probability-distribution-dependent parameter matrices is proposed. Based on the stochastic analysis techniques and the properties of the Kronecker product, delay-dependent synchronization stability criteria in the mean square are derived in the form of linear matrix inequalities which can be readily solved by using the LMI toolbox in MATLAB, the solvability of derived conditions depends on not only the size of the delay, but also the probability of the delay-taking values in some intervals. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

Non‐Fragile Synchronization Control For Markovian Jumping Complex Dynamical Networks With Probabilistic Time‐Varying Coupling Delays

“…Recently, in , authors have discussed the CDNs with probabilistic time varying delays. In , authors studied the synchronization problem of Markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time‐varying delays. The synchronization of discrete‐time stochastic complex networks with probabilistic interval time‐varying delays have been analyzed in .…”

“…Therefore, it is necessary to investigate the networks with probability distribution delay. Probability distribution of time delay in the interval is an important characteristic for the network conditions and was investigated in . The synchronization of Markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time‐varying delays have been investigated in .…”

“…Probability distribution of time delay in the interval is an important characteristic for the network conditions and was investigated in . The synchronization of Markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time‐varying delays have been investigated in . The synchronization of stability analysis for discrete‐time stochastic complex networks with probabilistic interval time‐varying delays were analyzed in .…”

Logic of Interval Uncertainty

“…A certain interest under this direction is generated by research in interval-dependent and interval-independent complex dynamical networks. There will be name worthy papers by Li and Yue (2010), as well as Li, Wong and Tang (2012), etc. Both publications do not only point out to an influence of the subordination factor between nodes of the network, directly preconditioning dependences, but also the time factor.…”

Bounded $H_{\infty}$ Synchronization and State Estimation for Discrete Time-Varying Stochastic Complex Networks Over a Finite Horizon

“…For example, in [26], the problem of stochastic synchronization analysis has been investigated for a new array of coupled discretetime stochastic complex networks with randomly occurred nonlinearities and time delays. The synchronization stability problem has been studied in [27] for a class of complex dynamical networks with Markovian jumping parameters and mixed time delays. In [28], the delay-distribution-dependent stability has been discussed for stochastic discrete-time neural networks with randomly mixed time-varying delays.…”