Existence and determination of the set of Metzler matrices for given stable polynomials

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2012)

  • Volume: 22, Issue: 2, page 389-399
  • ISSN: 1641-876X

Abstract

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The problem of the existence and determination of the set of Metzler matrices for given stable polynomials is formulated and solved. Necessary and sufficient conditions are established for the existence of the set of Metzler matrices for given stable polynomials. A procedure for finding the set of Metzler matrices for given stable polynomials is proposed and illustrated with numerical examples.

How to cite

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Tadeusz Kaczorek. "Existence and determination of the set of Metzler matrices for given stable polynomials." International Journal of Applied Mathematics and Computer Science 22.2 (2012): 389-399. <http://eudml.org/doc/208116>.

@article{TadeuszKaczorek2012,
abstract = {The problem of the existence and determination of the set of Metzler matrices for given stable polynomials is formulated and solved. Necessary and sufficient conditions are established for the existence of the set of Metzler matrices for given stable polynomials. A procedure for finding the set of Metzler matrices for given stable polynomials is proposed and illustrated with numerical examples.},
author = {Tadeusz Kaczorek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {determination; existence; Metzler matrix; polynomial; stability; existence and determination of Metzler matrices; stable polynomial},
language = {eng},
number = {2},
pages = {389-399},
title = {Existence and determination of the set of Metzler matrices for given stable polynomials},
url = {http://eudml.org/doc/208116},
volume = {22},
year = {2012},
}

TY - JOUR
AU - Tadeusz Kaczorek
TI - Existence and determination of the set of Metzler matrices for given stable polynomials
JO - International Journal of Applied Mathematics and Computer Science
PY - 2012
VL - 22
IS - 2
SP - 389
EP - 399
AB - The problem of the existence and determination of the set of Metzler matrices for given stable polynomials is formulated and solved. Necessary and sufficient conditions are established for the existence of the set of Metzler matrices for given stable polynomials. A procedure for finding the set of Metzler matrices for given stable polynomials is proposed and illustrated with numerical examples.
LA - eng
KW - determination; existence; Metzler matrix; polynomial; stability; existence and determination of Metzler matrices; stable polynomial
UR - http://eudml.org/doc/208116
ER -

References

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  2. Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London, 2002. Zbl1005.68175
  3. Benvenuti, L. and Farina, L. (2004). A tutorial on the positive realization problem, IEEE Transactions on Automatic Control 49(5): 651-664. 
  4. Kaczorek, T. (1992). Linear Control Systems, Vol.1, Research Studies Press, J. Wiley, New York, NY . Zbl0784.93002
  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 Sciences 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 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
  11. Kaczorek, T. (2008b). Realization problem for positive 2D hybrid systems, COMPEL 27 (3): 613-623. Zbl1148.93318
  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, 2009. 
  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/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/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. (2012). Determination of the set of Metzler matrices for given stable polynomials, PAK-Measurement, Automation and Monitoring (5), (in press). Zbl1283.93070
  20. 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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