Some conditions for convexifying static H control problems

Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier

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

2 Citations (Scopus)


In this paper, we show that a set of static controllers satisfying a certain level of H performance becomes convex when the underlying generalized plant satisfy several structural conditions. More precisely, we characterize such static H controllers by an LMI with the controller parameters being kept directly as decision variables. The conditions on the generalized plant are not too strict as illustrated by the fact that a sort of mixed sensitivity problems indeed satisfies these conditions. In addition, for the generalized plant of interest, we prove that full-order dynamical H controllers can be characterized by an LMI with simple change of variables. In stark contrast to known LMI formulations, the change of variables does not involve coefficient matrices of the generalized plant. This property is promising when dealing with a whole variety of robust control problems. As an illustration, the real μ synthesis problem is discussed.

Original languageEnglish
Title of host publicationProceedings of the 18th IFAC World Congress
PublisherIFAC Secretariat
Number of pages6
Edition1 PART 1
ISBN (Print)9783902661937
Publication statusPublished - 2011
Externally publishedYes

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
Number1 PART 1
ISSN (Print)1474-6670

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering


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