×

Exponential stability of the solutions of the initial value problem for systems with an impulse effect. (English) Zbl 0676.34035

The following three types of systems with impulse effects are considered:a) nonautonomous systems subjected to jumps at fixed points of time; b) the times of jumps depend on the state variable; c) the system is autonomous. Conditions are given under which the exponential stability of a given solution follows from the exponential stability of the respective system of variations.
Reviewer: L.Hatvani

MSC:

34D20 Stability of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] DOI: 10.1007/BF00945294 · Zbl 0612.34033
[2] LEELA S., Pacific J. Math. 55 pp 489– (1974)
[3] MIL’MAN V. D., Sib. math. J. 1 pp 233– (1960)
[4] PANDIT S. G., Differential Equations Involving Impulses (1982) · Zbl 0539.34001
[5] DOI: 10.1016/0022-247X(74)90174-7 · Zbl 0303.34042
[6] DOI: 10.1017/S0004972700008042 · Zbl 0372.34031
[7] SAMOILENKO A. M., Diff. Uravn. 13 pp 1995– (1977)
[8] DOI: 10.1016/0167-6911(83)90029-4 · Zbl 0529.93050
[9] ZAVAUŚĆIN S. T., Sr. –Ural. knizhn. Izd. (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.