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

• Published in: IEEE transactions on neural networks Vol. 21; no. 1; pp. 11 - 25
• Main Authors: Wang, Zidong, Wang, Yao, Liu, Yurong
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2010; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Complex networks; Computer science; control theory; systems; Computer Simulation; Computer systems and distributed systems. User interface; Couplings; Delay effects; Discrete time delays; distributed time delays; Disturbances; Exact sciences and technology; global synchronization; Humans; IP networks; Linear matrix inequalities; Networks; Neural Networks (Computer); Nonlinear Dynamics; Nonlinearity; randomly occurred nonlinearity (RON); Reaction Time; Signal Processing, Computer-Assisted; Software; stochastic complex networks; stochastic coupling; Stochastic Processes; Stochastic resonance; Stochastic systems; Stochasticity; Synchronism; Synchronization; Time delay; Time Factors; White noise; Working environment noise; global synchronization; Statistical analysis; Probabilistic approach; Stochastic matrix; distributed time delays; Complex system; Lyapunov method; Synchronization; Modeling; Delay; Discrete time delays; Network; Discrete time; White noise; Linear matrix inequality; stochastic complex networks; Matrix method; Delay time; Asymptotic approximation; Internet; randomly occurred nonlinearity (RON); stochastic coupling; Numerical algorithm; Lyapunov function
• ISSN: 1045-9227; 1941-0093; 1941-0093
• DOI: 10.1109/TNN.2009.2033599

In this paper, the problem of stochastic synchronization analysis is investigated for a new array of coupled discrete-time 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.