On Hankel Singular Values and Reflected Zeros of Linear Dynamical Systems

This note discusses a relationship between the Hankel singular values and reflected zeros of linear systems. Our main result proves that the Hankel singular values of a linear continuous-time system increase (decrease) pointwise when one or more zeros of the transfer function are reflected with resp...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2009-03, Vol.54 (3), p.641-646
Main Authors: Koshita, S., Abe, M., Kawamata, M., Antoulas, A.C.
Format: Article
Language:English
Subjects:
Applied sciences
Automatic control
Computer errors
Computer science
control theory
systems
Control theory. Systems
Dynamic range
Dynamical systems
Dynamics
Eigenvalues and eigenfunctions
Exact sciences and technology
Filters
H infinity control
Hankel singular values
linear continuous-time system
linear discrete-time system
Linear systems
Planes
Reduced order systems
reflected zeros
Signal processing
Transfer functions
Upper bound
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Description
Summary:This note discusses a relationship between the Hankel singular values and reflected zeros of linear systems. Our main result proves that the Hankel singular values of a linear continuous-time system increase (decrease) pointwise when one or more zeros of the transfer function are reflected with respect to the imaginary axis, that is, move from the left-(right-)half to the right-(left-)half of the complex plane. We also derive a similar result for linear discrete-time systems.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2008.2009687