Fractional controller based on a robust PI[alpha] observer for uncertain fractional systems

In this paper, we present a fractional sliding mode controller based on a robust [Formula omitted.] observer for fractional systems with bounded disturbances. This controller is introduced to achieve closed-loop Mittag-Leffler stability for uncertain fractional systems; meanwhile, the robust [Formul...

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Bibliographic Details
Published inInternational journal of systems science Vol. 50; no. 4; p. 829
Main Authors Trejo-Zúñiga, Iván, Delfín-Prieto, Sergio M, Martínez-Guerra, Rafael
Format Journal Article
LanguageEnglish
Published London Taylor & Francis Ltd 12.03.2019
Subjects
Control stability
Controllers
Liapunov functions
Mathematical analysis
Matrix methods
Robustness
Sliding mode control
Stability analysis
Twisting
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Summary:In this paper, we present a fractional sliding mode controller based on a robust [Formula omitted.] observer for fractional systems with bounded disturbances. This controller is introduced to achieve closed-loop Mittag-Leffler stability for uncertain fractional systems; meanwhile, the robust [Formula omitted.] observer is designed such that a [Formula omitted.] stability is obtained via quadratic Lyapunov functions and the tuning is achieved with linear matrix inequality approach. The performance and stability of the proposed controller are analysed and demonstrated through a generalised [Formula omitted.] -differentiator. Finally, to illustrate the effectiveness of the proposed approach a comparative analysis against the fractional Super-Twisting is carried out.
ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2019.1574043