Abstract
We consider the asymptotic stability problems by Lyapunov functionals V for a class of functional differential equations with impulses of the form x′(t)=f(t,x t ), x∈R n, t≧t 0, t≠t k ; △x=I k (t,x(t −)), t=t k , k∈Z +. Some new asymptotic stability results are presented by using an idea originated by Burton and Makay [6] and developed by Zhang [1]. We generalize some known results about impulsive functional differential equations in the literature in which we only require the derivative of V to be negative definite on a sequence of intervals I n =[s n ,ξ n ] which may or may not be contained in the sequence of impulsive time intervals [t n ,t n+1).
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Jiang, F., Shen, J. On the asymptotic stability for impulsive functional differential equations. Acta Math Hung 134, 307–321 (2012). https://doi.org/10.1007/s10474-011-0180-5
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DOI: https://doi.org/10.1007/s10474-011-0180-5