H∞ performance limitations analysis for SISO systems: A dual LMI approach

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

3 Citations (Scopus)

Abstract

In a very recent study by the first author and his colleagues, a novel LMI-based approach has been proposed to the best achievable H∞ performance limitations analysis for continuous-time SISO systems. Denoting by P and K a plant and a controller, respectively, and assuming that the plant P has an unstable zero, it was shown that a lower bound of the best achievable H∞ performance with respect to the transfer function (1+PK)-1P can be given analytically in terms of the real part of the unstable zero and the first non-zero coefficient of the Taylor expansion of P around the unstable zero. The goal of this paper is to show that, if the plant P has no unstable zeros except for the sole real unstable zero of degree one, then the lower bound shown there is exact. The exactness proof relies on the detailed analysis on the Lagrange dual problem of the SDP characterizing H∞ optimal controllers. More precisely, we show that we can construct an optimal dual solution proving the exactness analytically in terms of the state-space matrices of the plant P and the unstable zero. This analytical expression of the dual optimal solution is also a main result of this study.

Original languageEnglish
Title of host publication54rd IEEE Conference on Decision and Control,CDC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6629-6634
Number of pages6
ISBN (Electronic)9781479978861
DOIs
Publication statusPublished - Feb 8 2015
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: Dec 15 2015Dec 18 2015

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)0743-1546

Other

Other54th IEEE Conference on Decision and Control, CDC 2015
CountryJapan
CityOsaka
Period12/15/1512/18/15

Fingerprint

LMI Approach
Performance Analysis
Unstable
Continuous time systems
Controllers
Zero
Transfer functions
Exactness
Lower bound
Controller
Dual Solutions
Continuous-time Systems
Taylor Expansion
Dual Problem
Lagrange
Transfer Function
State Space
Optimal Solution
Coefficient

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

Ebihara, Y., Waki, H., & Sebe, N. (2015). H∞ performance limitations analysis for SISO systems: A dual LMI approach. In 54rd IEEE Conference on Decision and Control,CDC 2015 (pp. 6629-6634). [7403263] (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7403263

H∞ performance limitations analysis for SISO systems : A dual LMI approach. / Ebihara, Yoshio; Waki, Hayato; Sebe, Noboru.

54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 6629-6634 7403263 (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015).

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

Ebihara, Y, Waki, H & Sebe, N 2015, H∞ performance limitations analysis for SISO systems: A dual LMI approach. in 54rd IEEE Conference on Decision and Control,CDC 2015., 7403263, Proceedings of the IEEE Conference on Decision and Control, vol. 54rd IEEE Conference on Decision and Control,CDC 2015, Institute of Electrical and Electronics Engineers Inc., pp. 6629-6634, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japan, 12/15/15. https://doi.org/10.1109/CDC.2015.7403263
Ebihara Y, Waki H, Sebe N. H∞ performance limitations analysis for SISO systems: A dual LMI approach. In 54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 6629-6634. 7403263. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2015.7403263
Ebihara, Yoshio ; Waki, Hayato ; Sebe, Noboru. / H∞ performance limitations analysis for SISO systems : A dual LMI approach. 54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 6629-6634 (Proceedings of the IEEE Conference on Decision and Control).
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