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...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. II, Express briefs Express briefs, 2022-03, Vol.69 (3), p.1257-1261
Main Authors: Qian, Ruo-Nan, Lu, Jun-Guo, Zhang, Qing-Hao
Format: Article
Language:English
Subjects:
Circuits and systems
Eigenvalues and eigenfunctions
Fractional-order system
Invariants
linear time-invariant parameter-dependent system
maximal perturbation bound
Numerical stability
Parameters
Perturbation
Perturbation methods
Robust stability
Robustness (mathematics)
Stability criteria
Uncertainty
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Summary: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.
ISSN:1549-7747
1558-3791
DOI:10.1109/TCSII.2021.3119656