On H model reduction using LMIs

Yoshio Ebihara, Tomomichi Hagiwara

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


In this note, we deal with the problem of approximating a given nth-order linear time-invariant system G by an rth-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 linear matrix ineqaulity (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 note provides an alternative proof for those lower bounds via simple algebraic manipulations related to LMIs. 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
Pages (from-to)1187-1191
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number7
Publication statusPublished - Jul 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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