An elementary proof for the exactness of (D,G) scaling

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

1 Citation (Scopus)


The goal of this paper is to provide an elementary proof for the exactness of the (D,G) scaling applied to the uncertainty structure with one repeated real scalar block and one full complex matrix block. The (D,G) scaling has vast application area around control theory, optimization and signal processing. This is because, by applying the (D,G) scaling, we can convert inequality conditions depending on an uncertain parameter to linear matrix inequalities (LMIs) in an exact fashion. However, its exactness proof is tough, and this stems from the fact that the proof requires an involved matrix formula in addition to the standard Lagrange duality theory. To streamline the proof, in the present paper, we clarify that the involved matrix formula is closely related to a norm preserving dilation under structural constraints. By providing an elementary proof for the norm preserving dilation, it follows that basic results such as Schur complement and congruence transformation in conjunction with the Lagrange duality theory are enough to complete a self-contained exactness proof.

Original languageEnglish
Title of host publication2009 American Control Conference, ACC 2009
Number of pages6
Publication statusPublished - 2009
Externally publishedYes
Event2009 American Control Conference, ACC 2009 - St. Louis, MO, United States
Duration: Jun 10 2009Jun 12 2009

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2009 American Control Conference, ACC 2009
Country/TerritoryUnited States
CitySt. Louis, MO

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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