Passivity and Finite-Time Passivity for Multi-Weighted Fractional-Order Complex Networks With Fixed and Adaptive Couplings

This article presents several new alpha-passivity and alpha-finite-time passivity (alpha-FTP) concepts for the fractional-order systems with different input and output dimensions, which are distinct from the concepts for integer-order systems and extend the existing passivity and FTP definitions to some extent. On one hand, we not only develop some sufficient conditions for ensuring the alpha-passivity of the multi-weighted fractional-order complex dynamical networks (MWFOCDNs) with fixed and adaptive couplings, but also discuss the synchronization for the MWFOCDNs based on the alpha-output-strict passivity (alpha-OSP). On the other hand, the alpha-FTP for the MWFOCDNs with fixed and adaptive couplings are also studied on the basis of the designed state feedback controller, and the relationship between finite-time synchronization (FTS) and alpha-FTP for the MWFOCDNs is also illustrated. Finally, two numerical examples with simulation results are used to demonstrate the validity of the obtained criteria.

Automated summary

This article presents new concepts of alpha-passivity and alpha-finite-time passivity (alpha-FTP) for fractional-order systems with different input and output dimensions, extending existing definitions and conditions. The study develops sufficient conditions for alpha-passivity of multi-weighted fractional-order complex dynamical networks (MWFOCDNs) with fixed and adaptive couplings, and discusses synchronization based on alpha-output-strict passivity (alpha-OSP). Additionally, alpha-FTP for MWFOCDNs with fixed and adaptive couplings is studied using a designed state feedback controller, and the relationship between finite-time synchronization (FTS) and alpha-FTP is illustrated. The validity of the obtained criteria is demonstrated through numerical examples and simulation results.