Positive stable realizations of fractional continuous-time linear systems

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2011)

  • Volume: 21, Issue: 4, page 697-702
  • ISSN: 1641-876X

Abstract

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Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.

How to cite

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Tadeusz Kaczorek. "Positive stable realizations of fractional continuous-time linear systems." International Journal of Applied Mathematics and Computer Science 21.4 (2011): 697-702. <http://eudml.org/doc/208081>.

@article{TadeuszKaczorek2011,
abstract = {Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.},
author = {Tadeusz Kaczorek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fractional; positive; stable; realization; system Metzler matrix; procedure; linear continuous-time; fractional systems; positive stable realizations; linear continuous-time sytsems},
language = {eng},
number = {4},
pages = {697-702},
title = {Positive stable realizations of fractional continuous-time linear systems},
url = {http://eudml.org/doc/208081},
volume = {21},
year = {2011},
}

TY - JOUR
AU - Tadeusz Kaczorek
TI - Positive stable realizations of fractional continuous-time linear systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2011
VL - 21
IS - 4
SP - 697
EP - 702
AB - Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.
LA - eng
KW - fractional; positive; stable; realization; system Metzler matrix; procedure; linear continuous-time; fractional systems; positive stable realizations; linear continuous-time sytsems
UR - http://eudml.org/doc/208081
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
  5. Kaczorek, T. (2004). Realization problem for positive discretetime systems with delay, System Science 30(4): 117-130. 
  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 Siences 53(3): 293-298. Zbl1194.93128
  7. Kaczorek, T. (2006a). A realization problem for positive continuous-time 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 Siences 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). 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
  11. Kaczorek, T. (2008b). Realization problem for fractional continuous-time systems, Archives of Control Sciences 18(1): 43-58. Zbl1187.93019
  12. Kaczorek, T. (2008c). Realization problem for positive 2D hybrid systems, COMPEL 27(3): 613-623. Zbl1148.93318
  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. (2011). Selected Problems in Fractional Systems Theory, Springer-Verlag, Berlin. Zbl1221.93002
  16. Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, North-Holland, Amsterdam. Zbl1092.45003
  17. Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA. Zbl0924.34008
  18. 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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