On H∞ model reduction for discrete-time linear time-invariant systems using linear matrix inequalities

Yoshio Ebihara, Yoshito Hirai, Tomomichi Hagiwara

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

In this paper, we address the H∞ model reduction problem for linear time-invariant discrete-time systems. We revisit this problem by means of linear matrix inequality (LMI) approaches and first show a concise proof for the well-known lower bounds on the approximation error, which is given in terms of the Hankel singular values of the system to be reduced. In addition, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the H∞ optimal reduced-order model can readily be constructed via LMI optimization. These results can be regarded as complete counterparts of those recently obtained in the continuous-time system setting.
Original languageEnglish
Pages (from-to)291-300
Number of pages10
JournalAsian Journal of Control
Volume10
Issue number3
Publication statusPublished - May 2008

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