On model reduction using LMI's

Yoshio Ebihara, Tomomichi Hagiwara

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

2 Citations (Scopus)


In this paper, we deal with the problem of approximating a given n-th order LTI system G by an r-th order system Gr where r < n. It is shown that lower bounds of the H∞ norm of the associated error system can be analyzed by using LMI-related techniques. These lower bounds are given in terms of the Hankel singular values of the system G and coincide with those obtained in the previous studies where the analysis of the Hankel operators plays a central role. Thus, this paper provides an alternative proof for those lower bounds via simple algebraic manipulations related to LMI's. Moreover, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the problem is essentially convex and the optimal reduced-order models can be constructed via LMI optimization.

Original languageEnglish
Title of host publicationProceedings of the 2004 American Control Conference (AAC)
Number of pages6
Publication statusPublished - 2004
Externally publishedYes
EventProceedings of the 2004 American Control Conference (AAC) - Boston, MA, United States
Duration: Jun 30 2004Jul 2 2004

Publication series

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


ConferenceProceedings of the 2004 American Control Conference (AAC)
Country/TerritoryUnited States
CityBoston, MA

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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