An impulsive version of Perron's theorem
DOI:
https://doi.org/10.22199/S07160917.1993.0001.00004Abstract
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.
References
[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.
[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.
Published
2018-04-03
How to Cite
[1]
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.
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