A general solution to the output-zeroing problem for MIMO LTI systems

Jerzy Tokarzewski

International Journal of Applied Mathematics and Computer Science (2002)

  • Volume: 12, Issue: 2, page 161-171
  • ISSN: 1641-876X

Abstract

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The problem of zeroing the output in an arbitrary linear continuous-time system S(A,B,C,D) with a nonvanishing transfer function is discussed and necessary conditions for output-zeroing inputs are formulated. All possible real-valued inputs and real initial conditions which produce the identically zero system response are characterized. Strictly proper and proper systems are discussed separately.

How to cite

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Tokarzewski, Jerzy. "A general solution to the output-zeroing problem for MIMO LTI systems." International Journal of Applied Mathematics and Computer Science 12.2 (2002): 161-171. <http://eudml.org/doc/207576>.

@article{Tokarzewski2002,
abstract = {The problem of zeroing the output in an arbitrary linear continuous-time system S(A,B,C,D) with a nonvanishing transfer function is discussed and necessary conditions for output-zeroing inputs are formulated. All possible real-valued inputs and real initial conditions which produce the identically zero system response are characterized. Strictly proper and proper systems are discussed separately.},
author = {Tokarzewski, Jerzy},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {invariant zeros; output-zeroing problem; state-space methods; linear multivariable systems; linear system; output-zeroing input; zeros; zero module},
language = {eng},
number = {2},
pages = {161-171},
title = {A general solution to the output-zeroing problem for MIMO LTI systems},
url = {http://eudml.org/doc/207576},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Tokarzewski, Jerzy
TI - A general solution to the output-zeroing problem for MIMO LTI systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 2
SP - 161
EP - 171
AB - The problem of zeroing the output in an arbitrary linear continuous-time system S(A,B,C,D) with a nonvanishing transfer function is discussed and necessary conditions for output-zeroing inputs are formulated. All possible real-valued inputs and real initial conditions which produce the identically zero system response are characterized. Strictly proper and proper systems are discussed separately.
LA - eng
KW - invariant zeros; output-zeroing problem; state-space methods; linear multivariable systems; linear system; output-zeroing input; zeros; zero module
UR - http://eudml.org/doc/207576
ER -

References

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  3. Emami-Naeini A. and Van Dooren P. (1982): Computation of zeros of linear multivariable systems. - Automatica, Vol. 18, No. 4, pp. 415-430. Zbl0484.93029
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  5. Isidori A. (1995): Nonlinear Control Systems. - London: Springer. Zbl0878.93001
  6. Karcanias N. and Kouvaritakis B. (1979): The output-zeroing problem and its relationship to the invariant zero structure. - Int. J. Contr., Vol. 30, No. 3, pp. 395-415. Zbl0434.93018
  7. Latawiec K., Banka S. and Tokarzewski J. (2000): Control zeros and nonminimum phase LTI MIMO systems. - Ann. Rev. Contr., Vol. 24, pp. 105-112. 
  8. MacFarlane A.G.J. and Karcanias N. (1976): Poles and zeros of linear multivariable systems: A survey of the algebraic, geometric and complex variable theory. - Int. J. Contr., Vol. 24, No. 1, pp. 33-74. Zbl0374.93014
  9. Rosenbrock H.H. (1970): State Space and Multivariable Theory. - London: Nelson Zbl0246.93010
  10. Sontag E.D. (1990): Mathematical Control Theory. - New York: Springer. Zbl0703.93001
  11. Schrader C.B. and Sain M.K. (1989): Research on system zeros: A survey. - Int. J. Contr., Vol. 50, No. 4, pp. 1407-1433. Zbl0686.93036
  12. Tokarzewski J. (1998): System zeros analysis via the Moore-Penrose pseudoinverse and SVD of the first nonzero Markov parameter. - IEEE Trans. Automat. Contr., Vol. AC-43, No. 9, pp. 1285-1291. Zbl0957.93039
  13. Tokarzewski J. (2000a): A note on a general solution of the output - zeroing problem for MIMO LTI systems. - Proc. 6-th Int. Conf. Methods and Models in Automation and Robotics, MMAR'2000, Międzyzdroje, Poland, Vol. I, pp. 243-248. 
  14. Tokarzewski J. (2000b): A note on dynamical interpretation of invariant zeros in MIMO LTI systemsand algebraic criterions of degeneracy. - Proc. Int. Symp. Mathematical Theory of Networks and Systems, MTNS'2000, Perpignan, France, (on CD-ROM). 

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