# Realization problem for positive multivariable discretetime linear systems with delays in the state vector and inputs

International Journal of Applied Mathematics and Computer Science (2006)

- Volume: 16, Issue: 2, page 169-174
- ISSN: 1641-876X

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topKaczorek, Tadeusz. "Realization problem for positive multivariable discretetime linear systems with delays in the state vector and inputs." International Journal of Applied Mathematics and Computer Science 16.2 (2006): 169-174. <http://eudml.org/doc/207781>.

@article{Kaczorek2006,

abstract = {The realization problem for positive multivariable discrete-time systems with delays in the state and inputs is formulated and solved. Conditions for its solvability and the existence of a minimal positive realization are established. A procedure for the computation of a positive realization of a proper rational matrix is presented and illustrated with examples.},

author = {Kaczorek, Tadeusz},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {computation; discrete-time system; positive realization; existence; time delay; discrete-time systems},

language = {eng},

number = {2},

pages = {169-174},

title = {Realization problem for positive multivariable discretetime linear systems with delays in the state vector and inputs},

url = {http://eudml.org/doc/207781},

volume = {16},

year = {2006},

}

TY - JOUR

AU - Kaczorek, Tadeusz

TI - Realization problem for positive multivariable discretetime linear systems with delays in the state vector and inputs

JO - International Journal of Applied Mathematics and Computer Science

PY - 2006

VL - 16

IS - 2

SP - 169

EP - 174

AB - The realization problem for positive multivariable discrete-time systems with delays in the state and inputs is formulated and solved. Conditions for its solvability and the existence of a minimal positive realization are established. A procedure for the computation of a positive realization of a proper rational matrix is presented and illustrated with examples.

LA - eng

KW - computation; discrete-time system; positive realization; existence; time delay; discrete-time systems

UR - http://eudml.org/doc/207781

ER -

## References

top- Benvenuti L. and Farina L. (2004): A tutorial on the positive realization problem. - IEEE Trans. Automat. Contr., Vol. 49, No. 5, pp. 651-664.
- Busłowicz M. (1982): Explicit solution of discrete-delay equations. - Found. Contr. Eng., Vol. 7, No. 2, pp. 67-71. Zbl0526.34065
- Buslowicz M. and Kaczorek T. (2004): Reachability and minimum energy control of positive linear discrete-time systems with one delay. - Proc. 12th Mediterranean Conference Control and Automation, Kasadasi, Izmir, Turkey, (on CD-ROM). Zbl1140.93450
- Farina L. and Rinaldi S. (2000): Positive Linear Systems - Theory and Applications.- New York: Wiley. Zbl0988.93002
- Kaczorek T. (2002): Positive 1D and 2D Systems. - London: Springer. Zbl1005.68175
- Kaczorek T. (2003): Some recent developments in positive systems. - Proc. 7-th Conf.Dynamical Systems Theory and Applications, Łódź, Poland, pp. 25-35. Zbl1060.93057
- Kaczorek T. (2004): Realization problem for positive discrete-time systems with delay. - Syst. Sci., Vol. 30, No. 4, pp. 117-130.
- Kaczorek T. (2005): Realization problem for positive continuous-time systems with delays. - Proc. Int. Conf.Systems Engineering, Las Vegas, USA, (on CD-ROM). Zbl1127.93021
- Kaczorek T. and Busłowicz 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
- Klamka J. (1991): Controllability of Dynamical Systems. - Dordrecht: Kluwer. Zbl0732.93008
- Xie G. and Wang L. (2003): Reachability and controllability of positive linear discrete-time systems with time-delays, In: Positive Systems (L. Benvenuti, A. De Santis and L. Farina, Eds.). - Berlin: Springer, pp. 377-384. Zbl1067.93006

## Citations in EuDML Documents

top- Tadeusz Kaczorek, Positive stable realizations of fractional continuous-time linear systems
- Tadeusz Kaczorek, Existence and determination of the set of Metzler matrices for given stable polynomials
- Tadeusz Kaczorek, A modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays
- Tadeusz Kaczorek, Positive partial realization problem for linear discrete-time systems

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