On the general problem of stability for impulsive differential equations

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Abstract

Criteria for stability, asymptotical stability and instability of the nontrivial solutions of the impulsive system dx/dt = f(t, x), t ≠ θi(x), Δx t=θi(x) = Ii(x), i ∈ N = {1, 2,...}, where Δx t=θ := x(θ+) - x(θ, x(θ+) = limt→θ+ x(t) are obtained by Lyapunov's second method. The construction of a reduced system in the neighbourhood of a nontrivial solution is a central auxiliary result of the paper. © 2003 Elsevier Inc. All rights reserved.

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Akhmet, M. U. (2003). On the general problem of stability for impulsive differential equations. Journal of Mathematical Analysis and Applications, 288(1), 182–196. https://doi.org/10.1016/j.jmaa.2003.08.001

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