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Abstrakty
The question of how the classical concept of the Smith zeros of a 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 nonzero state-zero direction. Such a definition admits an infinite number of zeros (then the system is called degenerate). Algebraic criterions of degeneracy/nondegeneracy based on Weierstrass-Kronecker canonical form of the system and on the first nonzero Markov parameter are analyzed.
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Tom
Strony
61--78
Opis fizyczny
Bibliogr. 12 poz.,
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autor
- Military University of Technology, 00-908 Warsaw, Poland
Bibliografia
- [1] Banaszuk A., Kocięcki M., Lewis F. L., Kalman decomposition for implicit linear systems, lEEE Trans. Automat. Contr., Vol. 37, 1992, pp. 1509-1513.
- [2] Ben-Israel A., Greville T.N.E., Generalized Inverses: Theory and Applications, 2nd edition Wiley, New York 2002.
- [3] Gantmacher F. R., Theory of Matrices, Nauka, Moscow 1988, (in Russian).
- [4] Kaczorek T., Theory of Control and Systems, PWN, Warsaw 1999, (in Polish).
- [5] Kaczorek T., Positive One- and Two-dimensional Systems, Publishing House of the Warsaw University of Technology, Warsaw 2000, (in Polish).
- [6] Kaczorek T., Computation of fundamental matrices and reachability of positive singular discrete linear systems. Bulletin of the Polish Academy of Sciences, Technical Sciences, Vol. 46, No. 4 1998, pp. 501-511.
- [7] Misra P., Van Dooren P., Varga A., Computation of structural invariants of generalized state space systems, Automatica, Vol. 30, 1994, pp. 1921-1936.
- [8] Tokarzewski J., On some characterization of invariant and decoupling zeros in singular system. Archives of Control Sciences, Vol. 5, 1998, pp. 145-159.
- [9] Tokarzewski J., Zeros in Linear Systems: a Geometric Approach, Publishing House of the Warsaw University of Technology, Warsaw 2002.
- [10] Tokarzewski J., Relationship between Smith zeros and invariant zeros in linear singular system. Proc. 8th IEEE Int. Conf. Methods and Models in Automation and Robotics, MMAR'2002, Sept 2-5, 2002, Szczecin, Poland, Vol. I, pp. 71-74.
- [11] Dai L., Singular Control Systems, Springer-Verlag, Berlin-Tokyo, 1989.
- [12] Callier F. M., Desoer C. A., Multivariable Feedback Systems, Springer-Verlag, New York 1982.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BPW4-0002-0102