Dual LMI approach to H performance limitation analysis of sensitivity and complementary sensitivity functions

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

2 Citations (Scopus)

Abstract

In this paper, we study a dual-LMI-based approach to H performance limitation analysis of SISO systems. The scope includes the analysis of the sensitivity function S = (1 + PK)-1 and the complementary sensitivity function T = (1 + PK)-1 PK where P and K stand for the plant and the controller, respectively. The H performance limitations for these 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 (i.e., non-minimum phase zero) of degree one or the sole unstable pole of degree one. The goal of this paper is to show that such exact bounds can be reproduced by a dual LMI approach. To this end, we study a Lagrange dual of the standard SDP that is usually used to design H optimal controllers by numerical computation. By characterizing the structure of dual feasible solutions in terms of unstable zeros and unstable poles of the plant, we clarify that we can construct an optimal solution for the dual SDP analytically. It follows that we obtain exact H performance bounds that are consistent with the known results.

Original languageEnglish
Title of host publication2016 IEEE Conference on Computer Aided Control System Design, CACSD 2016 - Part of 2016 IEEE Multi-Conference on Systems and Control
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1440-1445
Number of pages6
ISBN (Electronic)9781509007592
DOIs
Publication statusPublished - Oct 19 2016
Event2016 IEEE Conference on Computer Aided Control System Design, CACSD 2016 - Buenos Aires, Argentina
Duration: Sep 19 2016Sep 22 2016

Publication series

NameProceedings of the IEEE International Symposium on Computer-Aided Control System Design
Volume2016-October
ISSN (Print)2165-3011
ISSN (Electronic)2165-302X

Other

Other2016 IEEE Conference on Computer Aided Control System Design, CACSD 2016
CountryArgentina
CityBuenos Aires
Period9/19/169/22/16

Fingerprint

LMI Approach
Performance Analysis
Poles and zeros
Controllers
Unstable
Performance Bounds
Transfer functions
Poles
Pole
Zero
Controller
Non-minimum Phase
Lagrange
Numerical Computation
Transfer Function
Closed-form
Optimal Solution

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Control and Optimization

Cite this

Ebihara, Y., Waki, H., & Sebe, N. (2016). Dual LMI approach to H performance limitation analysis of sensitivity and complementary sensitivity functions. In 2016 IEEE Conference on Computer Aided Control System Design, CACSD 2016 - Part of 2016 IEEE Multi-Conference on Systems and Control (pp. 1440-1445). [7602558] (Proceedings of the IEEE International Symposium on Computer-Aided Control System Design; Vol. 2016-October). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CACSD.2016.7602558

Dual LMI approach to H performance limitation analysis of sensitivity and complementary sensitivity functions. / Ebihara, Yoshio; Waki, Hayato; Sebe, Noboru.

2016 IEEE Conference on Computer Aided Control System Design, CACSD 2016 - Part of 2016 IEEE Multi-Conference on Systems and Control. Institute of Electrical and Electronics Engineers Inc., 2016. p. 1440-1445 7602558 (Proceedings of the IEEE International Symposium on Computer-Aided Control System Design; Vol. 2016-October).

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

Ebihara, Y, Waki, H & Sebe, N 2016, Dual LMI approach to H performance limitation analysis of sensitivity and complementary sensitivity functions. in 2016 IEEE Conference on Computer Aided Control System Design, CACSD 2016 - Part of 2016 IEEE Multi-Conference on Systems and Control., 7602558, Proceedings of the IEEE International Symposium on Computer-Aided Control System Design, vol. 2016-October, Institute of Electrical and Electronics Engineers Inc., pp. 1440-1445, 2016 IEEE Conference on Computer Aided Control System Design, CACSD 2016, Buenos Aires, Argentina, 9/19/16. https://doi.org/10.1109/CACSD.2016.7602558
Ebihara Y, Waki H, Sebe N. Dual LMI approach to H performance limitation analysis of sensitivity and complementary sensitivity functions. In 2016 IEEE Conference on Computer Aided Control System Design, CACSD 2016 - Part of 2016 IEEE Multi-Conference on Systems and Control. Institute of Electrical and Electronics Engineers Inc. 2016. p. 1440-1445. 7602558. (Proceedings of the IEEE International Symposium on Computer-Aided Control System Design). https://doi.org/10.1109/CACSD.2016.7602558
Ebihara, Yoshio ; Waki, Hayato ; Sebe, Noboru. / Dual LMI approach to H performance limitation analysis of sensitivity and complementary sensitivity functions. 2016 IEEE Conference on Computer Aided Control System Design, CACSD 2016 - Part of 2016 IEEE Multi-Conference on Systems and Control. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 1440-1445 (Proceedings of the IEEE International Symposium on Computer-Aided Control System Design).
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