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Tytuł artykułu

Relationship between Smith zeros and invariant zeros in linear systems

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EN
The question how the classical concept of the Smith zeros of a linear, time-invariant (LTI), multi-input, multi-output (MIMO) continuous-time singular system S (E, A, B, C, D) can be generalized and related to the stste-space methods is discussed. nothing is assumed about the relationship of the number of inputs to the number of outputs nor about the normal rank of the underlying system matrix. The aforementioned generalization treats zeros (called further the invariant zeros) as the triples . Such treatment is strictly connested with the output-zeroing problem and in that spirit the zeros can be easily interpreted even in the degenerate case.
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15--26
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
Bibliografia
  • [1] A. Banaszuk, M. Kociecki and F. L. Lewis: Kalman decomposition for implicit linear systems. IEEE Trans. AC., 37 1992, 1509-1513.
  • [2] G. Basile and G. Marro: Controlled and Conditioned Invariants in Linear Systems. Prentice-Hall, New York, 1992.
  • [3] A. Emami-Naeini and P. Van Dooren: Computation of Zeros of Linear Multivariable Systems. Automatica, 18 1982, 415-430.
  • [4] A. Isidori: Nonlinear Control Systems. Springer -Verlag, New York, 1995.
  • [5] T. Kaczorek: Theory of Control and Systems. Polish Scientific Publishers, Warsaw, 1999, (in Polish).
  • [6] T. Kaczorek: Positive Systems One and Twodimensional. Publishing House of Warsaw University of Technology, Warsaw, 2000, (in Polish).
  • [7] K. Latawiec, S. Banka And J. Tokarzewski: Control zeros and nonminimum phase LTI MIMO systems. Annual Reviews in Control, Pergamon, 24 2000, 105-112.
  • [8] A. G. J. Macfarlane and N. Karcanias: Poles and Zeros of Linear Multivariable Systems: a Survey of the Algebraic, Geometric and Complex Variable Theory. Int. J. Control, 24 1976, 33-74.
  • [9] P. Misra, P. Van Dooren and A. Varga: Computation of structural invariants of generalized state-space systems. Automatica, 30 1994, 1921-1936.
  • [10] H. H. Rosenbrock: The zeros of a system. Int. J. Control, 18 1973, 297-299.
  • [11] A. Saberi, B. M. Chen and P. Sannuti: Loop Transfer Recovery: Analysis and Design. Springer -Verlag, New York, 1993.
  • [12] C. B. Schrader and M. K. Sain: Research on system zeros: A survey. Int. J. Control, 50 1989, 1407-1433.
  • [13] E. D. Sontag: Mathematical Control Theory. Springer-Verlag, New York, 1990.
  • [14] J. Tokarzewski: On some characterization of invariant and decoupling zeros in singular systems. Archives of Control Sciences, 5 1998, 145-159.
  • [15] J. Tokarzewski: Zeros in Linear Systems: a Geometric Approach. Publishing House of Warsaw University of Technology, Warsaw, 2002.
  • [16] J. Tokarzewski: Relationship between Smith zeros and invariant zeros in linear singular systems. Proc. 8th IEEE Int. Conf. MMAR’2002, 2002, Szczecin, Poland, 71-74.
  • [17] W. M. Wonham: Linear Multivariable Control: a Geometric Approach. Springer-Verlag, New York, 1979.
  • [18] F. R. Gantmacher: Theory of Matrices. Nauka, Moscow, 1988 (in Russian).
  • [19] T. Kaczorek: Decomposition of singular linear systems. Przegląd Elektrotechniczny, 2 2003, 53-56.
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Bibliografia
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bwmeta1.element.baztech-article-BSW3-0009-0002
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