Dual LMI approach to H∞ performance limitations analysis of SISO systems with multiple unstable zeros and poles

Yoshio Ebihara, Shogo Shintani, Tomomichi Hagiwara

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

3 Citations (Scopus)

Abstract

In this paper, we study a dual-LMI-based approach to H∞ performance limitations analysis of SISO systems with multiple (i.e., duplicated) unstable zeros and poles. The scope includes the analysis of the transfer functions M = (1+PK)-1 P, S = (1+PK)-1, and T = (1+PK)-1 PK where P and K stand for the plant and the controller, respectively. The latter two transfer functions are well investigated, and exact closed-form performance bounds are already known for the cases where the plant has the sole unstable zero of degree one or the sole unstable pole of degree one. However, such exact bounds are hardly available for the cases where the plant has multiple (i.e., duplicated) unstable zeros and poles. To obtain a lower bound of the best achievable H∞ performance for such involved cases, in this paper, we study a dual of the standard LMI that represents the existence of H∞ controllers achieving a prescribed H∞ performance level. By deriving a parametrization of dual feasible solutions and constructing a dual suboptimal solution analytically, we can readily obtain a lower bound of the best achievable H∞ performance.

Original languageEnglish
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5638-5643
Number of pages6
ISBN (Electronic)9781467386821
DOIs
Publication statusPublished - Jul 28 2016
Externally publishedYes
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: Jul 6 2016Jul 8 2016

Publication series

NameProceedings of the American Control Conference
Volume2016-July
ISSN (Print)0743-1619

Conference

Conference2016 American Control Conference, ACC 2016
CountryUnited States
CityBoston
Period7/6/167/8/16

Fingerprint

Poles and zeros
Transfer functions
Controllers
Poles

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Ebihara, Y., Shintani, S., & Hagiwara, T. (2016). Dual LMI approach to H∞ performance limitations analysis of SISO systems with multiple unstable zeros and poles. In 2016 American Control Conference, ACC 2016 (pp. 5638-5643). [7526554] (Proceedings of the American Control Conference; Vol. 2016-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7526554

Dual LMI approach to H∞ performance limitations analysis of SISO systems with multiple unstable zeros and poles. / Ebihara, Yoshio; Shintani, Shogo; Hagiwara, Tomomichi.

2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 5638-5643 7526554 (Proceedings of the American Control Conference; Vol. 2016-July).

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

Ebihara, Y, Shintani, S & Hagiwara, T 2016, Dual LMI approach to H∞ performance limitations analysis of SISO systems with multiple unstable zeros and poles. in 2016 American Control Conference, ACC 2016., 7526554, Proceedings of the American Control Conference, vol. 2016-July, Institute of Electrical and Electronics Engineers Inc., pp. 5638-5643, 2016 American Control Conference, ACC 2016, Boston, United States, 7/6/16. https://doi.org/10.1109/ACC.2016.7526554
Ebihara Y, Shintani S, Hagiwara T. Dual LMI approach to H∞ performance limitations analysis of SISO systems with multiple unstable zeros and poles. In 2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 5638-5643. 7526554. (Proceedings of the American Control Conference). https://doi.org/10.1109/ACC.2016.7526554
Ebihara, Yoshio ; Shintani, Shogo ; Hagiwara, Tomomichi. / Dual LMI approach to H∞ performance limitations analysis of SISO systems with multiple unstable zeros and poles. 2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 5638-5643 (Proceedings of the American Control Conference).
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