Title :
On Hankel Singular Values and Reflected Zeros of Linear Dynamical Systems
Author :
Koshita, Shunsuke ; Abe, Masahide ; Kawamata, Masayuki ; Antoulas, Athanasios C.
Author_Institution :
Dept. of Electron. Eng., Tohoku Univ., Sendai
fDate :
3/1/2009 12:00:00 AM
Abstract :
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.
Keywords :
Hankel transforms; continuous time systems; discrete time systems; linear systems; time-varying systems; Hankel singular values; linear continuous-time system; linear discrete-time systems; linear dynamical systems; transfer function; Approximation error; Computer errors; Dynamic range; Eigenvalues and eigenfunctions; Filters; H infinity control; Linear systems; Reduced order systems; Signal processing; Transfer functions; Upper bound; Hankel singular values; linear continuous-time system; linear discrete-time system; reflected zeros;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2008.2009687
