Design of observer-based controllers for LPV systems with unknown parameters

W.P.M.H. Heemels, Jamal Daafouz, G. Millerioux

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Abstract

Output-based feedback control of LPV systemsis an important problem, as in practice it is rarely the case that the full state variable is available for feedback. In this paper we consider this problem in the case of discrete-time LPV systems for which the parameters are not exactly known, but only available with a finite accuracy or affected by noise during their measurement. The controllers are obtained usinga separate design of an observer and a state feedback and the interconnection is proven to stabilize the LPV system despite the mismatch between the true and available parameters. The approach allows to maximize the parameter uncertainty while still guaranteeing closed-loop stability. In addition, it is possibleto make tradeoffs between the admissible level of mismatch on the one hand and the performance in terms of decay factors on the other. All the design conditions will be formulated in term of LMIs, which can be solved efficiently, as is also illustratedby a numerical example.
Original languageEnglish
Title of host publicationProceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (CDC / CCC), 16-18 December 2009, Shanghai, China
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages1836-1841
DOIs
Publication statusPublished - 2009

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Controllers
State feedback
Feedback control
Feedback
Uncertainty

Cite this

Heemels, W. P. M. H., Daafouz, J., & Millerioux, G. (2009). Design of observer-based controllers for LPV systems with unknown parameters. In Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (CDC / CCC), 16-18 December 2009, Shanghai, China (pp. 1836-1841). Piscataway: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2009.5399793
Heemels, W.P.M.H. ; Daafouz, Jamal ; Millerioux, G. / Design of observer-based controllers for LPV systems with unknown parameters. Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (CDC / CCC), 16-18 December 2009, Shanghai, China. Piscataway : Institute of Electrical and Electronics Engineers, 2009. pp. 1836-1841
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Heemels, WPMH, Daafouz, J & Millerioux, G 2009, Design of observer-based controllers for LPV systems with unknown parameters. in Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (CDC / CCC), 16-18 December 2009, Shanghai, China. Institute of Electrical and Electronics Engineers, Piscataway, pp. 1836-1841. https://doi.org/10.1109/CDC.2009.5399793

Design of observer-based controllers for LPV systems with unknown parameters. / Heemels, W.P.M.H.; Daafouz, Jamal; Millerioux, G.

Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (CDC / CCC), 16-18 December 2009, Shanghai, China. Piscataway : Institute of Electrical and Electronics Engineers, 2009. p. 1836-1841.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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Heemels WPMH, Daafouz J, Millerioux G. Design of observer-based controllers for LPV systems with unknown parameters. In Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (CDC / CCC), 16-18 December 2009, Shanghai, China. Piscataway: Institute of Electrical and Electronics Engineers. 2009. p. 1836-1841 https://doi.org/10.1109/CDC.2009.5399793