Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed...

Area of Science:

• Control Systems Engineering
• Network Science
• Stochastic Systems

Background:

• Coupled complex networks are crucial in various systems, but their behavior is often affected by noise and delays.
• Existing models may not fully capture the dynamics of networks in real-world noisy environments like internet-based control systems.
• Stochastic synchronization is a key performance metric for network stability and information transmission.

Purpose of the Study:

• To investigate stochastic synchronization analysis for coupled discrete-time stochastic complex networks.
• To introduce randomly occurred nonlinearities (RONs) and multiple stochastic disturbances to model realistic network dynamics.
• To develop delay-dependent criteria for ensuring asymptotic synchronization in the mean square sense.

Main Methods:

• Construction of a novel Lyapunov-like matrix functional.
• Application of the delay fractioning technique.
• Utilization of linear matrix inequality (LMI) techniques, the free-weighting matrix method, and stochastic analysis theories.

Main Results:

• Several delay-dependent sufficient conditions for asymptotic synchronization in the mean square sense were derived.
• The derived criteria are formulated in terms of LMIs, solvable using standard numerical software.
• The proposed methods effectively address synchronization analysis in complex networks with RONs and time delays.

Conclusions:

• The study provides effective criteria for stochastic synchronization analysis in discrete-time complex networks with RONs and time delays.
• The developed LMI-based conditions are practical and computationally feasible.
• The findings contribute to the understanding and control of complex networks operating in noisy environments.