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.