The FCC Stability Criterion for Fractional-Order Linear Time-Invariant Systems with Commensurate or Incommensurate Orders

Arman Dabiri, Eric Butcher

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, a new stability criterion is proposed for the stability analysis of fractional-order linear time-invariant (FO-LTI) systems with incommensurate or commensurate orders. Although Matignon's theorem is well-established for studying the stability of FO-LTI systems with commensurate orders, there is no advanced and reliable criterion to check the stability of FO-LTI systems with incommensurate (not commensurate) orders. Therefore, developing a new criterion to check the stability of this type of FO-LTI systems is a necessity. The proposed criterion is based on constructing a monodromy operator for the solution of FO-LTI systems along with the use of short memory principle. Moreover, the monodromy operator is approximated by the use of the fractional Chebyshev collocation method, and necessary and sufficient conditions of the stability are obtained. The advantages of the proposed criterion are illustrated in three practical examples.

Original languageEnglish (US)
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2839-2844
Number of pages6
Volume2018-June
ISBN (Print)9781538654286
DOIs
StatePublished - Aug 9 2018
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: Jun 27 2018Jun 29 2018

Other

Other2018 Annual American Control Conference, ACC 2018
CountryUnited States
CityMilwauke
Period6/27/186/29/18

Fingerprint

Stability criteria
Data storage equipment

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Dabiri, A., & Butcher, E. (2018). The FCC Stability Criterion for Fractional-Order Linear Time-Invariant Systems with Commensurate or Incommensurate Orders. In 2018 Annual American Control Conference, ACC 2018 (Vol. 2018-June, pp. 2839-2844). [8431868] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2018.8431868

The FCC Stability Criterion for Fractional-Order Linear Time-Invariant Systems with Commensurate or Incommensurate Orders. / Dabiri, Arman; Butcher, Eric.

2018 Annual American Control Conference, ACC 2018. Vol. 2018-June Institute of Electrical and Electronics Engineers Inc., 2018. p. 2839-2844 8431868.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Dabiri, A & Butcher, E 2018, The FCC Stability Criterion for Fractional-Order Linear Time-Invariant Systems with Commensurate or Incommensurate Orders. in 2018 Annual American Control Conference, ACC 2018. vol. 2018-June, 8431868, Institute of Electrical and Electronics Engineers Inc., pp. 2839-2844, 2018 Annual American Control Conference, ACC 2018, Milwauke, United States, 6/27/18. https://doi.org/10.23919/ACC.2018.8431868
Dabiri A, Butcher E. The FCC Stability Criterion for Fractional-Order Linear Time-Invariant Systems with Commensurate or Incommensurate Orders. In 2018 Annual American Control Conference, ACC 2018. Vol. 2018-June. Institute of Electrical and Electronics Engineers Inc. 2018. p. 2839-2844. 8431868 https://doi.org/10.23919/ACC.2018.8431868
Dabiri, Arman ; Butcher, Eric. / The FCC Stability Criterion for Fractional-Order Linear Time-Invariant Systems with Commensurate or Incommensurate Orders. 2018 Annual American Control Conference, ACC 2018. Vol. 2018-June Institute of Electrical and Electronics Engineers Inc., 2018. pp. 2839-2844
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