Finite/Fixed-Time Pinning Synchronization of Complex Networks With Stochastic Disturbances

Abstract

This brief proposes a unified theoretical framework to investigate the finite/fixed-time synchronization of complex networks with stochastic disturbances. By designing a common pinning controller with different ranges of power parameters, both the goals of finite-time and fixed-time synchronization in probability for the network topology containing spanning trees can be achieved. Moveover, with the help of finite-time stochastic stability theory, two types of explicit expressions of finite/fixed (dependent/independent on the initial values) settling times are calculated as well. One numerical example is finally presented to demonstrate the effectiveness of the theoretical analysis.