A realization problem for positive continuoustime systems with reduced numbers of delays

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2006)

  • Volume: 16, Issue: 3, page 325-331
  • ISSN: 1641-876X

Abstract

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A realization problem for positive, continuous-time linear systems with reduced numbers of delays in state and in control is formulated and solved. Sufficient conditions for the existence of positive realizations with reduced numbers of delays of a given proper transfer function are established. A procedure for the computation of positive realizations with reduced numbers of delays is presented and illustrated by an example.

How to cite

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Kaczorek, Tadeusz. "A realization problem for positive continuoustime systems with reduced numbers of delays." International Journal of Applied Mathematics and Computer Science 16.3 (2006): 325-331. <http://eudml.org/doc/207796>.

@article{Kaczorek2006,
abstract = {A realization problem for positive, continuous-time linear systems with reduced numbers of delays in state and in control is formulated and solved. Sufficient conditions for the existence of positive realizations with reduced numbers of delays of a given proper transfer function are established. A procedure for the computation of positive realizations with reduced numbers of delays is presented and illustrated by an example.},
author = {Kaczorek, Tadeusz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {computation; continuous-time system; delay; positive realization; existence; continuous-time linear system},
language = {eng},
number = {3},
pages = {325-331},
title = {A realization problem for positive continuoustime systems with reduced numbers of delays},
url = {http://eudml.org/doc/207796},
volume = {16},
year = {2006},
}

TY - JOUR
AU - Kaczorek, Tadeusz
TI - A realization problem for positive continuoustime systems with reduced numbers of delays
JO - International Journal of Applied Mathematics and Computer Science
PY - 2006
VL - 16
IS - 3
SP - 325
EP - 331
AB - A realization problem for positive, continuous-time linear systems with reduced numbers of delays in state and in control is formulated and solved. Sufficient conditions for the existence of positive realizations with reduced numbers of delays of a given proper transfer function are established. A procedure for the computation of positive realizations with reduced numbers of delays is presented and illustrated by an example.
LA - eng
KW - computation; continuous-time system; delay; positive realization; existence; continuous-time linear system
UR - http://eudml.org/doc/207796
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. Buslowicz 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. 12-th Mediterranean Conf. 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. Galkowski K. (2001): State-Space Realizations of Linear 2D Systems with Extension to the General n D (n>2) Case. - Berlin: Springer. 
  6. Kaczorek T. (2002): Positive 1D and 2D Systems. - London: Springer. Zbl1005.68175
  7. Kaczorek T. (2003): Some recent developments in positive systems. - Proc. 7-th Conf. Dynamical Systems Theory and Applications, Lodz, Poland, pp. 25-35. Zbl1060.93057
  8. Kaczorek T. (2004): Realization problem for positive discrete-time systems with delay. - Syst. Sci., Vol. 30, No. 4, pp. 117-130. 
  9. Kaczorek T. (2005a): Realization problem for positive continuous-timesystems with delays. - Int. J. Comput. Intelligence and Appl., June 5, pp. 1-10. 
  10. Kaczorek T. (2005b): Realization problem for positive multivariable continuous-time systems with delays. - IEEE Trans. Automat. Contr., (submitted). Zbl1127.93021
  11. Kaczorek T. and Buslowicz 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
  12. Kaczorek T. and Buslowicz M. (2006): Reachability and minimum energy control of positive discrete-time linear systems with multiple delay in state and control. - Pomiary, Automatyka, Kontrola, PAK 78, pp. 31-33. 
  13. Xie G. and Wang L. (2003): Reachability and controllability of positive linear discrete-time systems with time-delays, In: Positive Systems, (Benvenuti L., De Santis A. and Farina L., Eds.). - LNCIS 294, Berlin: Springer-Verlag,pp. 377-384. Zbl1067.93006

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