Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays

Abstract

Abstract-In this paper, the problem of stochastic synchronization analysis is investigated for a new array of coupled discretetime stochastic complex networks with randomly occurred nonlinearities (RONs) and time delays. The discrete-time complex networks under consideration are subject to: 1) stochastic nonlinearities that occur according to the Bernoulli distributed white noise sequences; 2) stochastic disturbances that enter the coupling term, the delayed coupling term as well as the overall network; and 3) time delays that include both the discrete and distributed ones. Note that the newly introduced RONs and the multiple stochastic disturbances can better reflect the dynamical behaviors of coupled complex networks whose information transmission process is affected by a noisy environment (e.g., internet-based control systems). By constructing a novel Lyapunov-like matrix functional, the idea of delay fractioning is applied to deal with the addressed synchronization analysis problem. By employing a combination of the linear matrix inequality (LMI) techniques, the free-weighting matrix method and stochastic analysis theories, several delay-dependent sufficient conditions are obtained which ensure the asymptotic synchronization in the mean square sense for the discrete-time stochastic complex networks with time delays. The criteria derived are characterized in terms of LMIs whose solution can be solved by utilizing the standard numerical software. A simulation example is presented to show the effectiveness and applicability of the proposed results.

Impulsive control for synchronizing delayed discrete complex networks with switching topology

“…The results on complete synchronization, phase synchronization, space lag synchronization, and cluster reflect the ideas of [17–19]. The improvement on different regimes of synchronization of discrete complex networks is abstracted from papers authored by [9, 20]. Some general cases of synchronization of complex networks with switching topology can be found in the literatures of [15, 21].…”

Stability analysis for neutral-type impulsive neural networks with delays

“…We mention here that some finer approaches to deal with time delays would be the delay-slope-dependent method [21] and the delay-fraction approach [36], which could be the further work to reduce the possible conservatism in the dynamical analysis. And another future research topics would be the extension of the present results to more general cases, for example, the case that there exist multiply variable delays, and the case that the neural network of neutral-type is a difference system.…”

Synchronization of Chaotic Systems Using Sampled-Data Polynomial Controller

“…(11), we have _ VðtÞ Àz 1 ðtÞ T X 1 z 1 ðtÞ þ r 2 m e ðtÞ T X À1 1 m e ðtÞ (13) Considering the termination time of control t f [73][74][75] and taking integration on both sides of Eq. (13) with respect to time t, and recalling that z 1 ðtÞ ¼ X À1 1 eðtÞ, we obtain the following H 1 performance:…”

“…For exact synchronization [10][11][12][13][14], the system states of the response system will finally reach those of the drive ones. Various control approaches have been proposed for this category of chaotic synchronization.…”