A modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2012)

  • Volume: 22, Issue: 4, page 897-905
  • ISSN: 1641-876X

Abstract

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A new modified state variable diagram method is proposed for determination of positive realizations of linear continuoustime systems with delays in state and input vectors. Using the method, it is possible to find a positive realization with reduced numbers of delays for a given transfer matrix. Sufficient conditions for the existence of positive realizations of given proper transfer matrices are established. The proposed method is demonstrated on numerical examples.

How to cite

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Tadeusz Kaczorek. "A modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays." International Journal of Applied Mathematics and Computer Science 22.4 (2012): 897-905. <http://eudml.org/doc/244497>.

@article{TadeuszKaczorek2012,
abstract = {A new modified state variable diagram method is proposed for determination of positive realizations of linear continuoustime systems with delays in state and input vectors. Using the method, it is possible to find a positive realization with reduced numbers of delays for a given transfer matrix. Sufficient conditions for the existence of positive realizations of given proper transfer matrices are established. The proposed method is demonstrated on numerical examples.},
author = {Tadeusz Kaczorek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {state diagram method; determination; linear; continuous-time; delay; realization},
language = {eng},
number = {4},
pages = {897-905},
title = {A modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays},
url = {http://eudml.org/doc/244497},
volume = {22},
year = {2012},
}

TY - JOUR
AU - Tadeusz Kaczorek
TI - A modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays
JO - International Journal of Applied Mathematics and Computer Science
PY - 2012
VL - 22
IS - 4
SP - 897
EP - 905
AB - A new modified state variable diagram method is proposed for determination of positive realizations of linear continuoustime systems with delays in state and input vectors. Using the method, it is possible to find a positive realization with reduced numbers of delays for a given transfer matrix. Sufficient conditions for the existence of positive realizations of given proper transfer matrices are established. The proposed method is demonstrated on numerical examples.
LA - eng
KW - state diagram method; determination; linear; continuous-time; delay; realization
UR - http://eudml.org/doc/244497
ER -

References

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  2. Farina L. and Rinaldi S. (2000). Positive Linear Systems, Theory and Applications, J. Wiley, New York, NY. Zbl0988.93002
  3. Kaczorek T. (1992). Linear Control Systems, Vol.1, Research Studies Press, J. Wiley, New York, NY. Zbl0784.93002
  4. Kaczorek T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London. Zbl1005.68175
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  6. Kaczorek T. (2005). Positive minimal realizations for singular discrete-time systems with delays in state and delays in control, Bulletin of the Polish Academy of Sciences: Technical Sciences 53(3): 293-298. Zbl1194.93128
  7. Kaczorek T. (2006a). A realization problem for positive continuous-time linear systems with reduced numbers of delays, International Journal of Applied Mathematics and Computer Science 16(3): 325-331. Zbl1136.93317
  8. Kaczorek T. (2006b). Computation of realizations of discretetime cone systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 54(3): 347-350. Zbl1194.93129
  9. Kaczorek T. (2006c). Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs, International Journal of Applied Mathematics and Computer Science 16(2): 169-174. Zbl1111.93051
  10. Kaczorek T. (2008a). Realization problem for fractional continuous-time systems, Archives of Control Sciences 18(1): 43-58. Zbl1187.93019
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  12. Kaczorek T. (2008c). Fractional positive continuous-time linear systems and their reachability, International Journal of Applied Mathematics and Computer Science 18(2): 223-228, DOI: 10.2478/v10006-008-0020-0. Zbl1235.34019
  13. Kaczorek T. (2009a). Fractional positive linear systems, Kybernetes: The International Journal of Systems & Cybernetics 38(7/8): 1059-1078. Zbl1325.93033
  14. Kaczorek T. (2009b). Polynomial and Rational Matrices, Springer-Verlag, London. 
  15. Kaczorek T. (2011a). Computation of positive stable realizations for linear continuous-time systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 59(3): 273-281 and Proceedings of the 20th European Conference on Circuit Theory and Design, Linköping, Sweden. Zbl1291.93142
  16. Kaczorek T. (2011b). Positive stable realizations of fractional continuous-time linear systems, International Journal of Applied Mathematics and Computer Science 21(4): 697-702, DOI: 10.2478/v10006-011-0055-5. Zbl1283.93072
  17. Kaczorek T. (2011c). Positive stable realizations with system Metzler matrices, Archives of Control Sciences 21(2): 167-188 and Proceedings of the MMAR'2011 Conference, Międzyzdroje, Poland, (on CD-ROM). Zbl1270.93030
  18. Kaczorek T. (2011d). Selected Problems in Fractional Systems Theory, Springer-Verlag, London. Zbl1221.93002
  19. Kaczorek T. (2012a). Existence and determination of the set of Metzler matrices for given stable polynomials, International Journal of Applied Mathematics and Computer Science 22(2): 389-399, DOI: 10.2478/v10006-012-0029-2. Zbl1283.93070
  20. Kaczorek T. (2012b). Positive stable realizations of discrete-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(3): 605-616. 
  21. Shaker U. and Dixon M. (1977). Generalized minimal realization of transfer-function matrices, International Journal of Control 25(5): 785-803. Zbl0358.93007

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