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

• Autorzy: Tokarzewski J.
• Języki publikacji: EN

Abstrakty

EN

The question how the classical definition of the Smith zeros of an LTI continuous-time singular control system S(E,A,B,C,D) 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.

Słowa kluczowe

EN

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

PL

układ singularny; zera niezmienne; metoda przestrzeni stanu; parametry Markova

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2004
• Tom: Vol. 14, no 2
• Strony: 149--159
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Tokarzewski J.

• Military University of Technology, ul. Kaliskiego 2, 00-908 Warsaw, Poland,

Bibliografia

• [1] Callier F.M. and Desoer C.A. (1982): Multivariable Feedback Systems. — New York: Springer.
• [2] Ben-Israel A. and Greville T.N.E. (2002): Generalized Inverses: Theory and Applications, 2nd Ed. —New York: Wiley.
• [3] Dai L. (1989): Singular Control Systems. — Berlin: Springer.
• [4] Gantmacher F.R. (1988): Theory of Matrices. — Moscow: Nauka (in Russian).
• [5] 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.
• [6] Kaczorek T. (1999): Control and Systems Theory. — Warsaw: Polish Scientific Publishers (in Polish).
• [7] Kaczorek T. (2000): Positive One- and Two-Dimensional Systems. — Warsaw: University of Technology Press (in Polish).
• [8] Kaczorek T. (2003): Decomposition of singular linear systems. — Przegląd Elektrotechniczny, Vol. LXXIX, No. 2, pp. 53–58.
• [9] 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.
• [10] 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.
• [11] Tokarzewski J. (2002a): Zeros in Linear Systems: A Geometric Approach.—Warsaw: University of Technology Press.
• [12] 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.
• [13] 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.