Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
On the stability of certain perturbed systems of differential equations and the relationship with the magnitude of the perturbation
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Keywords

Polytope
Stability
Perturbation Norm
Politopo
Estabilidad
Norma de la perturbación

How to Cite

Vázquez Silva, E., & Monteiro Chissoca Chitungo, C. (2010). On the stability of certain perturbed systems of differential equations and the relationship with the magnitude of the perturbation. Revista De Matemática: Teoría Y Aplicaciones, 17(1), 13–24. https://doi.org/10.15517/rmta.v17i1.309

Abstract

In this work we consider a class of polytopes of third order square matrices, studied early. We obtain a condition to guarantee Hurwitz stability of each of elements of the polytope. This condition is more simples than one obtained before. Taking into account that to the considered set of matrices correspond a family of perturbed systems of differential equations, we study the relationship between the stability condition and the magnitude of the class of perturbations considered for this family.

https://doi.org/10.15517/rmta.v17i1.309
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References

Galeev, E.; Tijomirov, V. (1991) Breve Curso de la Teoría de Problemas Extremales. Editorial Mir, Moscú.

Hinrichsen, D.; Pritchard, A.J. (1988) “A robustness measure for linear systems under structured real parameter perturbations”, Report No. 184, Institut für Dynamische Systeme, Universität Bremen.

Kharitonov, V.L. (1978) “Asymptotic stability of an equilibrium position of a family of systems of linear differential equations”, Diffrentsial’nye Uravneniya 14(11).

Mederos, O.; Grau, R.; Hing, R.; González, L.A. (1987) Ecuaciones Diferenciales Ordinarias. Editorial Pueblo y Educación, Cuba.

Nicado, M. (1998) Estudio del Comportamiento de Sistemas de Control Automático de Tercer Orden con Perturbaciones Estacionarias y no Estacionarias. Tesis de Doctorado, Universidad Central de Las Villas, Villa Clara, Cuba.

Loan, C. van (1985) “How near is a stable matrix to an unstable matrix?”, Contemporary Math. 47.

Vázquez, E. (2002) “On the stability of class of polytopes of third order square matrices and stability radius”, Revista Matemática: Teoría y Aplicaciones 9(1): FALTA.

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