TY - GEN

T1 - On model reduction using LMI's

AU - Ebihara, Yoshio

AU - Hagiwara, Tomomichi

PY - 2004/11/29

Y1 - 2004/11/29

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=8744306250&partnerID=8YFLogxK

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U2 - 10.1109/ACC.2004.182342

DO - 10.1109/ACC.2004.182342

M3 - Conference contribution

AN - SCOPUS:8744306250

SN - 0780383354

T3 - Proceedings of the American Control Conference

SP - 774

EP - 779

BT - Proceedings of the 2004 American Control Conference (AAC)

T2 - Proceedings of the 2004 American Control Conference (AAC)

Y2 - 30 June 2004 through 2 July 2004

ER -