Positive partial realization problem for linear discrete-time systems

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2007)

  • Volume: 17, Issue: 2, page 165-171
  • ISSN: 1641-876X

Abstract

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A partial realization problem for positive linear discrete-time systems is addressed. Sufficient conditions for the existence of its solution are established. A procedure for the computation of a positive partial realization for a given finite sequence of the values of the impulse response is proposed. The procedure is illustrated by four numerical examples.

How to cite

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Kaczorek, Tadeusz. "Positive partial realization problem for linear discrete-time systems." International Journal of Applied Mathematics and Computer Science 17.2 (2007): 165-171. <http://eudml.org/doc/207828>.

@article{Kaczorek2007,
abstract = {A partial realization problem for positive linear discrete-time systems is addressed. Sufficient conditions for the existence of its solution are established. A procedure for the computation of a positive partial realization for a given finite sequence of the values of the impulse response is proposed. The procedure is illustrated by four numerical examples.},
author = {Kaczorek, Tadeusz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {computation; partial realization; discrete-time systems; positive systems; linear systems; existence},
language = {eng},
number = {2},
pages = {165-171},
title = {Positive partial realization problem for linear discrete-time systems},
url = {http://eudml.org/doc/207828},
volume = {17},
year = {2007},
}

TY - JOUR
AU - Kaczorek, Tadeusz
TI - Positive partial realization problem for linear discrete-time systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 2
SP - 165
EP - 171
AB - A partial realization problem for positive linear discrete-time systems is addressed. Sufficient conditions for the existence of its solution are established. A procedure for the computation of a positive partial realization for a given finite sequence of the values of the impulse response is proposed. The procedure is illustrated by four numerical examples.
LA - eng
KW - computation; partial realization; discrete-time systems; positive systems; linear systems; existence
UR - http://eudml.org/doc/207828
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. Farina L. and Rinaldi S. (2000): Positive Linear Systems: Theory and Applications.- Wiley, New York. Zbl0988.93002
  3. Ho B.L. and Kalman R.E. (1966): Effective construction of linear state-variable models from input/output functions. - Regelungstechnik, Bd.12, pp.545-548. Zbl0145.12701
  4. Kaczorek T. (1992): Linear Control Systems, Vol.1. - Taunton: Research Studies Press. Zbl0784.93002
  5. Kaczorek T. (2002): Positive 1D and 2D Systems. - London: Springer. Zbl1005.68175
  6. Kaczorek T. (2004): Realization problem for positive discrete-time systems with delay. - System Sci., Vol.30, No.4, pp.17-30. Zbl1087.93016
  7. Kaczorek T. (2005): Positive minimal realizations for singular discrete-time systems with delays in state and control. - Bull. Pol. Acad. Sci. Techn. Sci., Vol.53,No.3, pp.293-298. Zbl1194.93128
  8. Kaczorek T. (2006a): Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs. - Int. J. Appl. Math. Comput. Sci., Vol.16, No.2, pp.169-174. Zbl1111.93051
  9. Kaczorek T. (2006b) A realization problem for positive continuous-time linear systems with reduced number of delay. - Int. J. Appl. Math. Comput. Sci., Vol.16, No.3, pp.325-331. Zbl1136.93317
  10. Kaczorek T. (2006c): Computation of realizations of discrete-timecone-systems. - Bull. Polish Acad. Sci. Techn. Sci., Vol.54, No.3, pp.347-350. Zbl1194.93129
  11. Kaczorek T. (2006d): A realization problem for positive continuous-time systems with reduced numbers of delays.- Int. J. Appl. Math. Comput. Sci., Vol.16, No.3, pp.101-107. 
  12. KaczorekT. (2006e): Minimal positive realization for discrete-time systems with state time-delays. - Int. J. Comput. Math. Electr. Eng. COMPEL, Vol.25, No.4, pp.812-826. 
  13. Kaczorek T. and Buslowicz M. (2004): Minimal realization problem for positive multivariable linear systems with delay. - Int. J. Appl. Math. Comput. Sci.,Vol.14, No.2, pp.181-187. Zbl1076.93010
  14. Merzyakov J.I. (1963): On the existence of positive solutions of a system of linear equations. - Uspekhi Matematicheskikh Nauk, Vol.18, No.3, pp.179-186 (in Russian) 

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