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A note on zeros, output-nulling subspaces and zero-dynamics in MIMO LTI systems

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Abstrakty
EN
In a standard multi-input, multi-output linear time invariant (MIMO LTI) continuous-time system S9A,B,C) the classical notion of the Smith zeros does not characterize fully the output-zeroing problem nor the zero dynamics. The question how this notion can be extended and related to the state-space methods is discussed. Nothing is assumed about the ralationship of the number of inputs to the number of outputs nor about the normal rank of the underlying system matrix. The proposed extension treats multivariable zeros as the triples. Such a treatment is strictly connected with the output zeroing problem and in that spirit the zeros can be easily interpreted even in the degenerate case.
Rocznik
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179--199
Opis fizyczny
Bibliogr. poz. 23
Twórcy
Bibliografia
  • [1] G. Basile, G. Marro, Controlled and Conditioned Invariants in Linear System Theory, Prentice-Hall, Englewood Cliffs, NJ, 1992.
  • [2] F. M. Callier, C. A. Desoer, Multivariable Feedback Systems, Springer Verlag, New York, 1982.
  • [3] C. T. Chen, Linear System Theory and Design, Holt, Rinehart and Winston, New York, 1984.
  • [4] A. Emami-Naeini, P. Van Dooren, Computation of zeros of linear multivariable systems, Automatica, 18 (1982), pp. 415-430.
  • [5] F. R. Gantmacher, Theory of Matrices, Nauka, Moscow, 1988 (in Russian).
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  • [7] R. E. Kalman, On the computation of the reachable/observable canonical form, SIAM J. Contr.&Optimiz., 20 (1982), pp. 258-260.
  • [8] A. G. J. MacFarlane, N. Karcanias, Poles and zeros of linear multivariable systems: A survey of the algebraic, geometric and complex variable theory, Int. J. Contr., 24 (1976), pp. 33-74.
  • [9] P. Misra, P. Van Dooren, A. Varga, Computation of structural invariants of generalized state-space systems, Automatica, 30 (1994), pp. 1921-1936.
  • [10] G. Marro, Multivariable regulation in geometric terms: old and new results, in Colloquium on Automatic Control – Lecture Notes in Control and Information Sciences, C. Bonivento, G. Marro, R. Zanasi, Eds, vol.215, pp.77-138, Springer, London, 1996
  • [11] G. Marro, A. Piazzi – Feedback systems stabilizability in terms of invariant zeros,
  • [12] G. Marro, L. Ntogramatzidis, D, Prattichizzo, E. Zattoni, Linear Control Theory in geometric terms, CIRA Summer School „Antonio Ruberti”, Bertinoro, Italy, July 15-20, 2002
  • [13] H. H. Rosenbrock, State Space and Multivariable Theory, Nelson, London, 1970.
  • [14] H. H. Rosenbrock,The zeros of a system, Int.J.Contr., 18 (1973), pp. 297-299.
  • [15] C. B. Schrader, M. K. Sain, Research on system zeros: A survey, Int. J. Contr., 50 (1989), pp. 1407-1433.
  • [16] E. D. Sontag, Mathematical Control Theory, Springer-Verlag, New York, 1990.
  • [17] J. Tokarzewski, System zeros analysis via the Moore-Penrose pseudoinverse and SVD of the first nonzero Markov parameter, IEEE Trans., AC-43 (1998), pp. 1285-1291.
  • [18] J. Tokarzewski, A note on dynamical interpretation of invariant zeros in MIMO LTI systems and algebraic criterions of degeneracy, Int. Symp. MTNS, Perpignan, June 19-23, 2000 (compact disc).
  • [19] J. Tokarzewski, Zeros in Linear Systems: a Geometric Approach, Publishing House of the Warsaw University of Technology, Warsaw, 2002
  • [20] J. Tokarzewski – Realtionship between Smith zeros and invariant zeros in linear singular systems, Proc. of the 8th IEEE Int. Conf. On Methods and Models in Automation and Robotics, Sept. 2-5, 2002, Szczecin, Poland, vol. I, pp. 71-74
  • [21] W. M. Wonham, Linear Multivariable Control: a Geometric Approach, Springer-Verlag, New York, 1979.
  • [22] E. Zattoni, Output feedback regulation and model matching in geometric terms, CIRA Summer School „’Antonio Ruberti”, Bertinoro, Italy, July 15-20, 2002
  • [23] J. Tokarzewski: On invariant and Smith zeros, output-nulling subspaces and zero dynamics in MIMO LTI systems. Proc. of the 10th IEEE Int. Conf. On Methods and Models in Automation and Robotics. vol.I, (2004), 257-262
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSW3-0009-0011
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