Realization problem for positive multivariable discretetime linear systems with delays in the state vector and inputs

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2006)

  • Volume: 16, Issue: 2, page 169-174
  • ISSN: 1641-876X

Abstract

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The realization problem for positive multivariable discrete-time systems with delays in the state and inputs is formulated and solved. Conditions for its solvability and the existence of a minimal positive realization are established. A procedure for the computation of a positive realization of a proper rational matrix is presented and illustrated with examples.

How to cite

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Kaczorek, Tadeusz. "Realization problem for positive multivariable discretetime linear systems with delays in the state vector and inputs." International Journal of Applied Mathematics and Computer Science 16.2 (2006): 169-174. <http://eudml.org/doc/207781>.

@article{Kaczorek2006,
abstract = {The realization problem for positive multivariable discrete-time systems with delays in the state and inputs is formulated and solved. Conditions for its solvability and the existence of a minimal positive realization are established. A procedure for the computation of a positive realization of a proper rational matrix is presented and illustrated with examples.},
author = {Kaczorek, Tadeusz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {computation; discrete-time system; positive realization; existence; time delay; discrete-time systems},
language = {eng},
number = {2},
pages = {169-174},
title = {Realization problem for positive multivariable discretetime linear systems with delays in the state vector and inputs},
url = {http://eudml.org/doc/207781},
volume = {16},
year = {2006},
}

TY - JOUR
AU - Kaczorek, Tadeusz
TI - Realization problem for positive multivariable discretetime linear systems with delays in the state vector and inputs
JO - International Journal of Applied Mathematics and Computer Science
PY - 2006
VL - 16
IS - 2
SP - 169
EP - 174
AB - The realization problem for positive multivariable discrete-time systems with delays in the state and inputs is formulated and solved. Conditions for its solvability and the existence of a minimal positive realization are established. A procedure for the computation of a positive realization of a proper rational matrix is presented and illustrated with examples.
LA - eng
KW - computation; discrete-time system; positive realization; existence; time delay; discrete-time systems
UR - http://eudml.org/doc/207781
ER -

References

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  1. Benvenuti L. and Farina L. (2004): A tutorial on the positive realization problem. - IEEE Trans. Automat. Contr., Vol. 49, No. 5, pp. 651-664. 
  2. Busłowicz M. (1982): Explicit solution of discrete-delay equations. - Found. Contr. Eng., Vol. 7, No. 2, pp. 67-71. Zbl0526.34065
  3. Buslowicz M. and Kaczorek T. (2004): Reachability and minimum energy control of positive linear discrete-time systems with one delay. - Proc. 12th Mediterranean Conference Control and Automation, Kasadasi, Izmir, Turkey, (on CD-ROM). Zbl1140.93450
  4. Farina L. and Rinaldi S. (2000): Positive Linear Systems - Theory and Applications.- New York: Wiley. Zbl0988.93002
  5. Kaczorek T. (2002): Positive 1D and 2D Systems. - London: Springer. Zbl1005.68175
  6. Kaczorek T. (2003): Some recent developments in positive systems. - Proc. 7-th Conf.Dynamical Systems Theory and Applications, Łódź, Poland, pp. 25-35. Zbl1060.93057
  7. Kaczorek T. (2004): Realization problem for positive discrete-time systems with delay. - Syst. Sci., Vol. 30, No. 4, pp. 117-130. 
  8. Kaczorek T. (2005): Realization problem for positive continuous-time systems with delays. - Proc. Int. Conf.Systems Engineering, Las Vegas, USA, (on CD-ROM). Zbl1127.93021
  9. Kaczorek T. and Busłowicz M. (2004): Minimal realization for positive multivariable linear systems with delay. - Int. J. Appl. Math. Comput. Sci., Vol. 14, No. 2, pp. 181-187. Zbl1076.93010
  10. Klamka J. (1991): Controllability of Dynamical Systems. - Dordrecht: Kluwer. Zbl0732.93008
  11. Xie G. and Wang L. (2003): Reachability and controllability of positive linear discrete-time systems with time-delays, In: Positive Systems (L. Benvenuti, A. De Santis and L. Farina, Eds.). - Berlin: Springer, pp. 377-384. Zbl1067.93006

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