17th International Symposium on
Mathematical Theory of Networks and Systems
Kyoto International Conference Hall, Kyoto, Japan, July 24-28, 2006

MTNS 2006 Paper Abstract

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Paper MoP05.3

Ebihara, Yoshio (Kyoto Univ.), Hirai, Yoshito (Kyoto Univ.), Hagiwara, Tomomichi (Kyoto Univ.)

On H-Infinity Model Reduction for Discrete-Time LTI Systems Using LMIs

Scheduled for presentation during the Regular Session "Model reduction" (MoP05), Monday, July 24, 2006, 16:10−16:35, Room F

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on March 28, 2024

Keywords Model reduction, Convex optimization

Abstract

In this paper, we address the H-infinity 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 of 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-infinity 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 setting.