Singular perturbation approximation of balanced systems
作者:
YI LIU,
BRIAND. O. ANDERSON,
期刊:
International Journal of Control
(Taylor Available online 1989)
卷期:
Volume 50,
issue 4
页码: 1379-1405
ISSN:0020-7179
年代: 1989
DOI:10.1080/00207178908953437
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
This paper relates the singular perturbation approximation technique for model reduction to the direct truncation technique if the system model to be reduced is stable, minimal and internally balanced. It shows that these two methods constitute two fully compatible model-reduction techniques for a continuous-time system, and both methods yield a stable, minimal and internally balanced reduced-order system with the same L∞-norm error bound on the reduction. Although the upper bound for both reductions is the same, the direct truncation method tends to have smaller errors at high frequencies and larger errors at low frequencies, while the singular perturbation approximation method will display the opposite character. It also shows that a certain bilinear mapping not only preserves the balanced structure between a continuous-time system and an associated discrete-time system, but also preserves the slow singular perturbation approximation structure. Hence the continuous-time results on the singular perturbation approximation of balanced systems are easily extended to the discrete-time case. Examples are used to show the compatibility and the differences in the two reduction techniques for a balanced system
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