The realization problem for a class of positive, continuous-time linear SISO systems with one delay is formulated and solved. Sufficient conditions for the existence of positive realizations of a given proper transfer function are established. A procedure for the computation of positive minimal realizations is presented and illustrated by an example.
@article{bwmeta1.element.bwnjournal-article-amcv15i4p447bwm,
author = {Kaczorek, Tadeusz},
title = {Realization problem for a class of positive continuous-time systems with delays},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {15},
year = {2005},
pages = {447-453},
zbl = {1127.93021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv15i4p447bwm}
}
Kaczorek, Tadeusz. Realization problem for a class of positive continuous-time systems with delays. International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) pp. 447-453. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv15i4p447bwm/
[000] Benvenuti L. and Farina L. (2004): A tutorial on the positive realization problem. - IEEE Trans. Automat. Contr., Vol. 49, No. 5, pp. 651-664.
[001] Buslowicz M. (1982): Explicit solution of discrete-delay equations. - Found. Contr. Eng., Vol. 7, No. 2, pp. 67-71. | Zbl 0526.34065
[002] 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,i Kasadasi, Izmir, Turkey, (on CD-ROM). | Zbl 1140.93450
[003] Farina L. and Rinaldi S.(2000): Positive Linear Systems, Theory and Applications. - New York: Wiley. | Zbl 0988.93002
[004] Kaczorek T. (2002): Positive 1D and 2D Systems. - London: Springer. | Zbl 1005.68175
[005] Kaczorek T. (2003): Some recent developments in positive systems. - Proc. 7-th Conf. Dynamical Systems Theory and Applications, Łódź, Poland, pp. 25-35. | Zbl 1060.93057
[006] 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. | Zbl 1076.93010
[007] 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. | Zbl 1067.93006