A Lower Bound for the Balanced Truncation Error for MIMO Systems

被引：8

作者：

Opmeer, Mark R. ^{[1
]}

Reis, Timo ^{[2
]}

机构：

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] Univ Hamburg, Dept Math, D-20146 Hamburg, Germany

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2015年 / 60卷 / 08期

关键词：

Balanced realization; balanced truncation; error bound; Hankel operator; linear time-invariant systems; model reduction; SINGULAR PERTURBATION APPROXIMATION; MODEL-REDUCTION; LINEAR-SYSTEMS; PASSIVITY; SYMMETRY;

D O I：

10.1109/TAC.2014.2368232

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We show that for a class of systems which includes state space symmetric systems, the balanced truncation error is bounded from below by twice the sum of the tail of the Hankel singular values (including multiplicities) divided by the dimension of the input space.

引用

页码：2207 / 2212

页数：6

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