Strong feasibility of the dual problem of linear matrix inequality for H output feedback control problem

Hayato Waki, Noboru Sebe

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

1 Citation (Scopus)

Abstract

Strong feasibility (a.k.a. strict feasibility) of the dual problem of a given linear matrix inequality (LMI) is an important property to guarantee the existence of an optimal solution of the LMI problem. In particular, the LMI problem may not have any optimal solutions if the dual is not strongly feasible. This implies that the computed solutions by SDP solvers may be meaningless and useless for designing the controllers of H output feedback control problems. The facial reduction is a tool to analyze and reduce such non-strongly feasible problems. We introduce the strong feasibility of the dual and facial reduction and provide the necessary and sufficient condition on the strong feasibility. Furthermore, we reveal that the condition is closely related to invariant zeros in the plant.

Original languageEnglish
Title of host publicationSICE ISCS 2018 - 2018 SICE International Symposium on Control Systems
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages47-53
Number of pages7
ISBN (Electronic)9784907764586
DOIs
Publication statusPublished - Apr 2 2018
Event2018 SICE International Symposium on Control Systems, SICE ISCS 2018 - Tokyo, Japan
Duration: Mar 9 2018Mar 11 2018

Publication series

NameSICE ISCS 2018 - 2018 SICE International Symposium on Control Systems
Volume2018-January

Other

Other2018 SICE International Symposium on Control Systems, SICE ISCS 2018
CountryJapan
CityTokyo
Period3/9/183/11/18

Fingerprint

Output Feedback Control
Dual Problem
Linear matrix inequalities
Feedback control
Matrix Inequality
Linear Inequalities
Control Problem
Optimal Solution
Controllers
Controller
Imply
Necessary Conditions
Invariant
Sufficient Conditions
Zero

All Science Journal Classification (ASJC) codes

  • Process Chemistry and Technology
  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering
  • Control and Optimization

Cite this

Waki, H., & Sebe, N. (2018). Strong feasibility of the dual problem of linear matrix inequality for H output feedback control problem. In SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems (pp. 47-53). (SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/SICEISCS.2018.8330155

Strong feasibility of the dual problem of linear matrix inequality for H output feedback control problem. / Waki, Hayato; Sebe, Noboru.

SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems. Institute of Electrical and Electronics Engineers Inc., 2018. p. 47-53 (SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems; Vol. 2018-January).

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

Waki, H & Sebe, N 2018, Strong feasibility of the dual problem of linear matrix inequality for H output feedback control problem. in SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems. SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems, vol. 2018-January, Institute of Electrical and Electronics Engineers Inc., pp. 47-53, 2018 SICE International Symposium on Control Systems, SICE ISCS 2018, Tokyo, Japan, 3/9/18. https://doi.org/10.23919/SICEISCS.2018.8330155
Waki H, Sebe N. Strong feasibility of the dual problem of linear matrix inequality for H output feedback control problem. In SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems. Institute of Electrical and Electronics Engineers Inc. 2018. p. 47-53. (SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems). https://doi.org/10.23919/SICEISCS.2018.8330155
Waki, Hayato ; Sebe, Noboru. / Strong feasibility of the dual problem of linear matrix inequality for H output feedback control problem. SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 47-53 (SICE ISCS 2018 - 2018 SICE International Symposium on Control Systems).
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