The question how the classical definition of the Smith zeros of an LTI continuous-time singular control system can be generalized and related to state-space methods is discussed. The zeros are defined as those complex numbers for which there exists a zero direction with a nonzero state-zero direction. Such a definition allows an infinite number of zeros (then the system is called degenerate). A sufficient and necessary condition for nondegeneracy is formulated. Moreover, some characterization of invariant zeros, based on the Weierstrass-Kronecker canonical form of the system and the first nonzero Markov parameter, is obtained.
@article{bwmeta1.element.bwnjournal-article-amcv14i2p149bwm,
author = {Tokarzewski, Jerzy},
title = {A note on some characterization of invariant zeros in singular systems and algebraic criteria of nondegeneracy},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {14},
year = {2004},
pages = {149-159},
zbl = {1076.93021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv14i2p149bwm}
}
Tokarzewski, Jerzy. A note on some characterization of invariant zeros in singular systems and algebraic criteria of nondegeneracy. International Journal of Applied Mathematics and Computer Science, Tome 14 (2004) pp. 149-159. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv14i2p149bwm/
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