Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.apnum.2004.01.013
Title: A numerically reliable solution for the squaring-down problem in system design
Authors: Chu, D. 
Hung, Y.S.
Keywords: Compensator
Infinite zero
Invariant zero
Orthogonal transformation
Squaring-down
Issue Date: Nov-2004
Citation: Chu, D., Hung, Y.S. (2004-11). A numerically reliable solution for the squaring-down problem in system design. Applied Numerical Mathematics 51 (2-3) : 221-241. ScholarBank@NUS Repository. https://doi.org/10.1016/j.apnum.2004.01.013
Abstract: In this paper, matrix pencil theory is used to study the squaring-down problem where a linear time-invariant system with an unequal number of inputs and outputs is turned into an invertible square system with an equal number of inputs and outputs. Both static and dynamic compensators are considered for squaring down. In the case of static compensation, the infinite-zero structure of the original system is preserved after squaring down. In the case of dynamic compensation, key system properties including stabilizability, detectability and the infinite-zero structure of the original system are also preserved after squaring down. Furthermore, one can additionally assign the invariant zeros induced by squaring down to the open left half plane, provided that the original system is stabilizable and detectable. This means that squaring down by dynamic compensation preserves minimum phaseness as well. The preservation of these system properties is highly desirable for subsequent feedback design of the squared-down system. Unlike existing squaring-down methods which do not address the issue of numerical properties, our solution is based on a condensed form derived using only orthogonal transformations which are numerically stable. Explicit formulas which can be implemented in a numerically reliable manner are given for determining the squaring-down compensators. Examples are presented to illustrate the numerical superiority of the proposed method. © 2004 IMACS. Publishesd by Elsevier B.V. All Rights reserved.
Source Title: Applied Numerical Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/102724
ISSN: 01689274
DOI: 10.1016/j.apnum.2004.01.013
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

5
checked on May 18, 2018

WEB OF SCIENCETM
Citations

5
checked on Mar 21, 2018

Page view(s)

42
checked on May 11, 2018

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.