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2004 | 14 | 2 | 149-159
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
14
Numer
2
Strony
149-159
Opis fizyczny
Daty
wydano
2004
otrzymano
2003-07-18
poprawiono
2004-03-24
Twórcy
  • Military University of Technology, ul. Kaliskiego 2, 00-908 Warsaw, Poland
Bibliografia
  • Callier F.M. and Desoer C.A. (1982): Multivariable Feedback Systems. - New York: Springer.
  • Ben-Israel A. and Greville T.N.E. (2002): Generalized Inverses: Theory and Applications, 2nd Ed. - New York: Wiley.
  • Dai L. (1989): Singular Control Systems. - Berlin: Springer.
  • Gantmacher F.R. (1988): Theory of Matrices. - Moscow: Nauka (in Russian).
  • Kaczorek T. (1998): Computation of fundamental matrices and reachability of positive singular discrete linear systems. - Bull. Polish Acad. Sci. Techn. Sci., Vol. 46, No. 4, pp. 501-511.
  • Kaczorek T. (1999): Control and Systems Theory. - Warsaw: Polish Scientific Publishers (in Polish).
  • Kaczorek T. (2000): Positive One- and Two-Dimensional Systems. -Warsaw: University of Technology Press (in Polish).
  • Kaczorek T. (2003): Decomposition of singular linear systems. - Przegląd Elektrotechniczny, Vol. LXXIX, No. 2, pp. 53-58.
  • Misra P., Van Dooren P. and Varga A. (1994): Computation of structural invariants of generalized state-space systems. - Automatica, Vol. 30, No. 12, pp. 1921-1936.
  • 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.
  • Tokarzewski J. (2002a): Zeros in Linear Systems: A Geometric Approach.- Warsaw: University of Technology Press.
  • 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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Bibliografia
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bwmeta1.element.bwnjournal-article-amcv14i2p149bwm
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