TY - GEN
T1 - Bounds of imaginary spectra for the stability assessment of a class of fractional-order systems with multiple delays
AU - Cai, Jiazhi
AU - Liu, Yifan
AU - Shi, Lingling
AU - Gao, Qingbin
N1 - Publisher Copyright:
© 2021 IEEE
PY - 2021
Y1 - 2021
N2 - We treat the stability problem of a general class of fractional-order systems with multiple delays from a new perspective. To start with, we build a one-to-one correspondence between the imaginary spectra of original fractional-order systems and the special imaginary spectra of transformed systems with the auxiliary variable. Next, we show a novel improved frequency sweeping algorithm by using the Dixon resultant concept (IFS-DR) to calculate the so-called kernel hypersurfaces (KH). With these, the complete stability map is constructed by the Cluster Treatment of Characteristic Roots (CTCR) paradigm. We show that our presented approaches are valid and effective by the case study. In addition, the obtained stability map is compared to that of an integer-order time-delayed system. Finally, the results are verified by the Simulinkbased simulations.
AB - We treat the stability problem of a general class of fractional-order systems with multiple delays from a new perspective. To start with, we build a one-to-one correspondence between the imaginary spectra of original fractional-order systems and the special imaginary spectra of transformed systems with the auxiliary variable. Next, we show a novel improved frequency sweeping algorithm by using the Dixon resultant concept (IFS-DR) to calculate the so-called kernel hypersurfaces (KH). With these, the complete stability map is constructed by the Cluster Treatment of Characteristic Roots (CTCR) paradigm. We show that our presented approaches are valid and effective by the case study. In addition, the obtained stability map is compared to that of an integer-order time-delayed system. Finally, the results are verified by the Simulinkbased simulations.
KW - CTCR
KW - Dixon resultant theory
KW - Fractional-order systems
KW - stability analysis
UR - http://www.scopus.com/inward/record.url?scp=85128047984&partnerID=8YFLogxK
U2 - 10.1109/CAC53003.2021.9728505
DO - 10.1109/CAC53003.2021.9728505
M3 - Conference contribution
AN - SCOPUS:85128047984
T3 - Proceeding - 2021 China Automation Congress, CAC 2021
SP - 1850
EP - 1855
BT - Proceeding - 2021 China Automation Congress, CAC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2021 China Automation Congress, CAC 2021
Y2 - 22 October 2021 through 24 October 2021
ER -