Distributed Synchronization for Nonlinear Coupled Stochastic Networks with Time Delays Using Randomly Occurring Control

The study focuses on distributed synchronization in<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>a type of stochastic complex dynamical network characterized by time-varying delays and nonlinear coupling, subject to randomly occurring control. The proposed design involves a distributed adaptive controller with randomly occurring activation and control gain updates. By employing LaSalle's invariance principle, Lyapunov stability theory, the properties of the Kronecker product of matrices, etc., an appropriate Lyapunov functional is constructed to derive the criteria for synchronization in mean square for such networks.