# A note on some characterization of invariant zeros in singular systems and algebraic criteria of nondegeneracy

International Journal of Applied Mathematics and Computer Science (2004)

- Volume: 14, Issue: 2, page 149-159
- ISSN: 1641-876X

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topTokarzewski, 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 14.2 (2004): 149-159. <http://eudml.org/doc/207686>.

@article{Tokarzewski2004,

abstract = {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.},

author = {Tokarzewski, Jerzy},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {Markov parameters; singular control systems; state-space methods; multivariable zeros},

language = {eng},

number = {2},

pages = {149-159},

title = {A note on some characterization of invariant zeros in singular systems and algebraic criteria of nondegeneracy},

url = {http://eudml.org/doc/207686},

volume = {14},

year = {2004},

}

TY - JOUR

AU - Tokarzewski, Jerzy

TI - A note on some characterization of invariant zeros in singular systems and algebraic criteria of nondegeneracy

JO - International Journal of Applied Mathematics and Computer Science

PY - 2004

VL - 14

IS - 2

SP - 149

EP - 159

AB - 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.

LA - eng

KW - Markov parameters; singular control systems; state-space methods; multivariable zeros

UR - http://eudml.org/doc/207686

ER -

## References

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- Tokarzewski J. (1998): On some characterization of invariant and decoupling zeros in singular systems. - Arch. Contr. Sci., Vol. 5, No. 3-4, pp. 145-159. Zbl1193.93106
- Tokarzewski J. (2002a): Zeros in Linear Systems: A Geometric Approach.- Warsaw: University of Technology Press. Zbl1044.93036
- Tokarzewski J. (2002b): Relationship between Smith zeros and invariant zeros in linear singular systems. - Proc. 8th IEEE Int. Conf. Methods and Models in Automation and Robotics, MMAR 2002, Szczecin, Poland, Vol. I, pp. 71-74.
- Tokarzewski J. (2003): A characterization of invariant zeros in singular systems via the first nonzero Markov parameter and algebraic criterions of nondegeneracy. - Proc. 9th IEEE Int. Conf. Methods and Models in Automation and Robotics, MMAR 2003, Międzyzdroje, Poland, Vol. I, pp. 437-442.

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