An impulsive version of Perron's theorem


  • Víctor H. Cortes Universidad de Chile.
  • Patricio González Universidad de Chile.



We prove the asymptolic stability of the null solution of the impulsive system x' = Ax+ f(t, x) under the influence of externa linear impulses defined by constant matrices {Dj }j. These matrices act at a given fixed and increasing unbonnded sequence of positive times {lj }j· The main idea is to apply a generalization of Bellman's inequality lo such impulsive system.

Author Biographies

Víctor H. Cortes, Universidad de Chile.

Departamento de Matemáticas.

Patricio González, Universidad de Chile.

Departamento de Matemáticas.


[1] Coddington, E.A.; Levinson, N.. Theory of Ordinary Differential Equations. McGraw-Hill Book Co, 1955.

[2] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P.S.: Theory of Impulsie Differential Equations. Wolrd Scientific Publishing Co, 1989.

[3] Milev, N.N.; Bainov, D.D.: Stability of Linear lmpulsive Differential Equations. lnt. J. Syslems S. C. I. 21 (1990), 2217-2224.

[4] Perron, O.: Uber Stabilität und Asymptotisches Verhalten der lntegrale von Differentialgleichungssystemem. Math. Zeit. 29 ( 1929), 129-160.



How to Cite

V. H. Cortes and P. González, “An impulsive version of Perron’s theorem”, Proyecciones (Antofagasta, On line), vol. 12, no. 1, pp. 35-43, Apr. 2018.