Estabilidad de sistemas lineales positivos por politopos invariantes
DOI:
https://doi.org/10.36788/sah.v7i1.136Palabras clave:
Sistemas Positivos, Politopo Convexo, Invarianza Positiva.Resumen
El objetivo principal de este artículo es describir la estabilidad de sistemas lineales positivos mediante politopos invariantes en el espacio de estados, de forma que a cada sistema estable le corresponde una familia de politopos invariantes. Además, para el caso del plano, presentamos una manera de estabilizar sistemas lineales positivos mediante el diseño de controles lineales.
Descargas
Citas
A. Bacciotti and L. Rosier, Liapunov functions and stability in control theory. Springer Science & Business Media, 2005. DOI: https://doi.org/10.1007/b139028
Z. Bartosiewicz, “Stability and stabilization of linear positive systems on time scales,” Positivity, vol. 24, no. 5, pp. 1361–1372, 2020. DOI: 10.1007/s11117-020-00735-z DOI: https://doi.org/10.1007/s11117-020-00735-z
A. Berman and R. J. Plemmons, Nonnegative matrices in the mathematical sciences. SIAM, 1994. DOI: https://doi.org/10.1137/1.9781611971262
N. P. Bhatia and G. P. Szegö, Stability theory of dynamical systems. Springer Science & Business Media, 2002. DOI: https://doi.org/10.1007/978-3-642-62006-5_2
S. P. Bhattacharyya and L. H. Keel, “Robust control: the parametric approach,” in Advances in control education 1994. Elsevier, 1995, pp. 49–52. DOI: https://doi.org/10.1016/B978-0-08-042230-5.50016-5
V. S. Bokharaie, O. Mason, and F. Wirth, “Stability and positivity of equilibria for subhomogeneous cooperative systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 17, pp. 6416–6426, 2011. DOI: 10.1016/j.na.2011.06.023 DOI: https://doi.org/10.1016/j.na.2011.06.023
E. B. Castelan and J.-C. Hennet, “On invariant polyhedra of continuous-time linear systems,” IEEE Transactions on Automatic control, vol. 38, no. 11, pp. 1680–1685, 1993. DOI: 10.1109/9.262058 DOI: https://doi.org/10.1109/9.262058
B. Du, S. Xu, Z. Shu, and Y. Chen, “On positively invariant polyhedrons for continuous-time positive linear systems,” Journal of the Franklin Institute, vol. 357, no. 17, pp. 12 571–12 587, 2020. DOI: 10.1016/j.jfranklin.2020.05.013 DOI: https://doi.org/10.1016/j.jfranklin.2020.05.013
A. C. Enthoven and K. J. Arrow, “A Theorem on Expectations and the Stability of Equilibrium,” Econometrica: Journal of the Econometric Society, pp. 288–293, 1956. DOI: 10.2307/1911633 DOI: https://doi.org/10.2307/1911633
A. Fall, A. Iggidr, G. Sallet, and J.-J. Tewa, “Epidemiological models and Lyapunov functions,” Mathematical Modelling of Natural Phenomena, vol. 2, no. 1, pp. 62–83, 2007. DOI: 10.1051/mmnp:2008011 DOI: https://doi.org/10.1051/mmnp:2008011
L. Farina and S. Rinaldi, Positive linear systems: theory and applications. John Wiley & Sons, 2000, vol. 50. DOI: https://doi.org/10.1002/9781118033029
Z. Horváth, Y. Song, and T. Terlaky, “A Novel Unified Approach to Invariance for a Dynamical System,” arXiv preprint arXiv:1405.5167, 2014. DOI: 10.48550/arXiv.1405.5167
W. Leontief, Input-output economics. Oxford University Press, 1986. DOI: https://doi.org/10.1057/978-1-349-95121-5_1072-1
H. Leyva, G. Quiroz, F. Carrillo, and R. Femat, “Rapid insulin stabilization via sliding modes control for T1DM therapy,” in Memorias del Congreso Nacional de Control Automática AMCA, 2013.
H. Leyva, F. A. Carrillo, G. Quiroz, and R. Femat, “Robust stabilization of positive linear systems via sliding positive control,” Journal of Process Control, vol. 41, pp. 47–55, 2016. DOI: 10.1016/j.jprocont.2016.03.001 DOI: https://doi.org/10.1016/j.jprocont.2016.03.001
D. G. Luenberger, Introduction to dynamic systems: theory, models, and applications. Wiley New York, 1979, vol. 1.
M. W. McConley, B. D. Appleby, M. A. Dahleh, and E. Feron, “A control Lyapunov function approach to robust stabilization of nonlinear systems,” in Proceedings of the 1997 American Control Conference (Cat. No. 97CH36041), vol. 1. IEEE, 1997, pp. 329–333. DOI: https://doi.org/10.1109/ACC.1997.611811
G. Quiroz and R. Femat, “On hyperglicemic glucose basal levels in Type 1 Diabetes Mellitus from dynamic analysis,” Mathematical biosciences, vol. 210, no. 2, pp. 554–575, 2007. DOI: 10.1016/j.mbs.2007.06.004 DOI: https://doi.org/10.1016/j.mbs.2007.06.004
A. Rantzer, “Scalable control of positive systems,” European Journal of Control, vol. 24, pp. 72–80, 2015. DOI: 10.1016/j.ejcon.2015.04.004 DOI: https://doi.org/10.1016/j.ejcon.2015.04.004
R. T. Rockafellar, Convex analysis. Princeton university press, 1997, vol. 11.
J. T. Sorensen, “A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes,” Ph.D. dissertation, Massachusetts Institute of Technology, 1985.
G. M. Ziegler, Lectures on polytopes. Springer New York, NY, 1995. DOI: https://doi.org/10.1007/978-1-4613-8431-1
Descargas
Publicado
Cómo citar
Número
Sección
Licencia
Derechos de autor 2023
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.
Los artículos publicados por Sahuarus. Revista Electrónica de Matemáticas se distribuye bajo una Licencia Creative Commons Atribución-NoComercial-SinDerivadas 4.0 Internacional, la cual permite la distribución y el uso del material publicado citando la fuente de la que proviene, prohibe la modificación y el uso con fines comerciales.
