# A realization problem for positive continuoustime systems with reduced numbers of delays

International Journal of Applied Mathematics and Computer Science (2006)

- Volume: 16, Issue: 3, page 325-331
- ISSN: 1641-876X

## Access Full Article

top## Abstract

top## How to cite

topKaczorek, Tadeusz. "A realization problem for positive continuoustime systems with reduced numbers of delays." International Journal of Applied Mathematics and Computer Science 16.3 (2006): 325-331. <http://eudml.org/doc/207796>.

@article{Kaczorek2006,

abstract = {A realization problem for positive, continuous-time linear systems with reduced numbers of delays in state and in control is formulated and solved. Sufficient conditions for the existence of positive realizations with reduced numbers of delays of a given proper transfer function are established. A procedure for the computation of positive realizations with reduced numbers of delays is presented and illustrated by an example.},

author = {Kaczorek, Tadeusz},

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

keywords = {computation; continuous-time system; delay; positive realization; existence; continuous-time linear system},

language = {eng},

number = {3},

pages = {325-331},

title = {A realization problem for positive continuoustime systems with reduced numbers of delays},

url = {http://eudml.org/doc/207796},

volume = {16},

year = {2006},

}

TY - JOUR

AU - Kaczorek, Tadeusz

TI - A realization problem for positive continuoustime systems with reduced numbers of delays

JO - International Journal of Applied Mathematics and Computer Science

PY - 2006

VL - 16

IS - 3

SP - 325

EP - 331

AB - A realization problem for positive, continuous-time linear systems with reduced numbers of delays in state and in control is formulated and solved. Sufficient conditions for the existence of positive realizations with reduced numbers of delays of a given proper transfer function are established. A procedure for the computation of positive realizations with reduced numbers of delays is presented and illustrated by an example.

LA - eng

KW - computation; continuous-time system; delay; positive realization; existence; continuous-time linear system

UR - http://eudml.org/doc/207796

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.
- Buslowicz 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. 12-th Mediterranean Conf. 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
- Galkowski K. (2001): State-Space Realizations of Linear 2D Systems with Extension to the General $nD$ (n>2) Case. - Berlin: Springer.
- 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, Lodz, 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. (2005a): Realization problem for positive continuous-timesystems with delays. - Int. J. Comput. Intelligence and Appl., June 5, pp. 1-10.
- Kaczorek T. (2005b): Realization problem for positive multivariable continuous-time systems with delays. - IEEE Trans. Automat. Contr., (submitted). Zbl1127.93021
- Kaczorek T. and Buslowicz 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
- Kaczorek T. and Buslowicz M. (2006): Reachability and minimum energy control of positive discrete-time linear systems with multiple delay in state and control. - Pomiary, Automatyka, Kontrola, PAK 78, pp. 31-33.
- Xie G. and Wang L. (2003): Reachability and controllability of positive linear discrete-time systems with time-delays, In: Positive Systems, (Benvenuti L., De Santis A. and Farina L., Eds.). - LNCIS 294, Berlin: Springer-Verlag,pp. 377-384. Zbl1067.93006

## Citations in EuDML Documents

top- Tadeusz Kaczorek, Positive partial realization problem for linear discrete-time systems
- 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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.