Adaptive Control for Finite-Time Cluster Synchronization of Fractional-Order Fully Complex-Valued Dynamical Networks

Abstract

This paper aims to address finite-time cluster synchronization (FTCS) issues for fractional-order fully complex-valued dynamical networks (FFCVDNs) with time delay. To compensate for the limited application of one controller, the delay-dependent and delay-independent adaptive controllers with regard to quadratic and absolute-valued norms are developed, respectively. Based on the finite-time stability theorem and auxiliary inequality techniques, detailed Lyapunov analysis is provided to ensure that FFCVDNs can achieve FTCS, and the settling times (STs) are estimated on the basis of system and control parameters characterized by system models to decrease the conservativeness of the existing results. Finally, simulation examples are provided to verify the correctness of theoretical analysis.

Keywords

• complex-valued dynamical networks
• finite-time stability
• adaptive control
• cluster synchronization