Maximal Perturbation Bounds for the Robust Stability of Fractional-Order Linear Time-Invariant Parameter-Dependent Systems

This brief investigates the maximal perturbation bounds of fractional-order linear time-invariant parameter-dependent systems with the commensurate order
$\alpha \in (0,1)$
. Firstly, new sufficient and necessary conditions for the maximal perturbation bounds of such parameter-dependent systems with the single parameter are given using the Kronecker sum. Secondly, the results with the single parameter case are extended to the cases with the multiple parameters. Ultimately numerical examples are presented to verify that the proposed methods in this brief are valid.