Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.
@article{bwmeta1.element.bwnjournal-article-amcv21i4p697bwm,
author = {Tadeusz Kaczorek},
title = {Positive stable realizations of fractional continuous-time linear systems},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {21},
year = {2011},
pages = {697-702},
zbl = {1283.93072},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv21i4p697bwm}
}
Tadeusz Kaczorek. Positive stable realizations of fractional continuous-time linear systems. International Journal of Applied Mathematics and Computer Science, Tome 21 (2011) pp. 697-702. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv21i4p697bwm/
[000] Benvenuti, L. and Farina, L. (2004). A tutorial on the positive realization problem, IEEE Transactions on Control 49(5): 651-664.
[001] Farina, L. and Rinaldi, S. (2000). Positive Linear Systems, Theory and Applications, J. Wiley, New York, NY. | Zbl 0988.93002
[002] Kaczorek, T. (1992). Linear Control Systems, Vol. 1, Research Studies Press, J. Wiley, New York, NY. | Zbl 0784.93002
[003] Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London. | Zbl 1005.68175
[004] Kaczorek, T. (2004). Realization problem for positive discretetime systems with delay, System Science 30(4): 117-130.
[005] 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 Siences 53(3): 293-298. | Zbl 1194.93128
[006] 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. | Zbl 1136.93317
[007] Kaczorek, T. (2006b). Computation of realizations of discretetime cone systems, Bulletin of the Polish Academy of Sciences: Technical Siences 54(3): 347-350. | Zbl 1194.93129
[008] 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. | Zbl 1111.93051
[009] Kaczorek, T. (2008a). 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. | Zbl 1235.34019
[010] Kaczorek, T. (2008b). Realization problem for fractional continuous-time systems, Archives of Control Sciences 18(1): 43-58. | Zbl 1187.93019
[011] Kaczorek, T. (2008c). Realization problem for positive 2D hybrid systems, COMPEL 27(3): 613-623. | Zbl 1148.93318
[012] Kaczorek, T. (2009a). Fractional positive linear systems, Kybernetes: The International Journal of Systems & Cybernetics 38 (7/8): 1059-1078. | Zbl 1325.93033
[013] Kaczorek, T. (2009b). Polynomial and Rational Matrices, Springer-Verlag, London.
[014] Kaczorek, T. (2011). Selected Problems in Fractional Systems Theory, Springer-Verlag, Berlin. | Zbl 1221.93002
[015] Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, North-Holland, Amsterdam. | Zbl 1092.45003
[016] Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA. | Zbl 0924.34008
[017] Shaker, U. and Dixon, M. (1977). Generalized minimal realization of transfer-function matrices, International Journal of Control 25(5): 785-803. | Zbl 0358.93007