Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.
@article{bwmeta1.element.bwnjournal-article-amcv23z3p501bwm, author = {Tadeusz Kaczorek}, title = {Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {23}, year = {2013}, pages = {501-506}, zbl = {1279.93062}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv23z3p501bwm} }
Tadeusz Kaczorek. Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems. International Journal of Applied Mathematics and Computer Science, Tome 23 (2013) pp. 501-506. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv23z3p501bwm/
[000] Berman, A. and Plemmons, R.J. (1994). Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA. | Zbl 0815.15016
[001] Busłowicz, M. (2008). Stability of linear continuous-time fractional order systems with delays of the retarded type, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 319-324.
[002] Busłowicz, M. (2012). Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(2): 279-284.
[003] Busłowicz, M. and Kaczorek, T. (2009). Simple conditions for practical stability of positive fractional discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 19(2): 263-269, DOI: 10.2478/v10006-009-0022-6. | Zbl 1167.93019
[004] Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY. | Zbl 0988.93002
[005] Gantmakher, F.R. (1959). Theory of Matrices, Chelsea Pub. Co., New York, NY. | Zbl 0050.24804
[006] Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London. | Zbl 1005.68175
[007] Kaczorek, T. (1999). Relationship between the value of discretisation step and positivity and stabilization of linear dynamic systems, Proceedings of the Conference on Simulation, Designing and Control of Foundry Processes, Kraków, Poland, pp. 33-39.
[008] Kaczorek, T. (1998). Vectors and Matrices in Automation and Electrotechnics, WNT, Warsaw, (in Polish).
[009] Kaczorek, T. (2011). Selected Problems of Fractional System Theory, Springer-Verlag, Berlin. | Zbl 1221.93002
[010] Kaczorek, T. (2013). Approximation of positive stable continuous-time linear systems by positive stable discrete-time systems, Pomiary Automatyka Robotyka 59 (2): 359-364. | Zbl 1279.93062
[011] Kaczorek, T. (2011). Necessary and sufficient conditions of stability of fractional positive continuous-time linear systems, Acta Mechanica et Automatica 5(2): 52-54.