An impulsive version of Perron's theorem

• Cortes, Víctor H. ^[1] ; González, Patricio ^[1]
  1. [1] Universidad de Chile

     Universidad de Chile

     Santiago, Chile

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 12, Nº. 1, 1993, págs. 35-43
• Idioma: inglés
• DOI: 10.22199/S07160917.1993.0001.00004
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• Resumen

  • 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.

• Referencias bibliográficas
  • Citas [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.