Finite-Time Cluster Synchronization of Delayed Fractional-Order Fully Complex-Valued Community Networks

Abstract

This paper focuses on the finite-time (FNT) cluster synchronization issues for a class of delayed fractional-order fully complex-valued community networks (FFCVCNs). A new mathematical expression of the complex networks is developed with internal delay, non-delayed and delayed couplings, complex-valued state variables, system function, coupling strengths, inner coupling matrices and outer coupling matrices. Instead of transforming the complex-valued (CV) networks into two independent real-valued (RV) systems, the delay-dependent controllers are designed based on the quadratic norm and a novel norm composed of the absolute-valued norm to realize the cluster synchronization for the proposed complex networks in FNT, respectively. In addition, the upper bounds of the settling time (ST) when the system could reach finite-time cluster synchronization are estimated. The obtained results are less conservative than some of the existing studies due to the characteristics of fully fractional-order complex-valued (FOCV) dynamical networks. The feasibility and effectiveness of the main results are demonstrated by simulation examples.

Keywords

• Finite-time synchronization
• cluster synchronization
• fully complex-valued community networks
• delay