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

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    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