Stability of the Zero Solution of Impulsive Differential Equations by the Lyapunov Second Method
Stability of the Zero Solution of Impulsive Differential Equations by the Lyapunov Second Method
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DOI：
10.1006/jmaa.2000.6864
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发表时间：
2000-08
影响因子：
1.3
通讯作者：
M. Akhmetov;A. Zafer
中科院分区：
文献类型：
--
作者：
M. Akhmetov;A. Zafer
本文讨论了脉冲系统dx dt = ft，x，t <$θ ix Δx零解的稳定性|t = θ i（x）= J i x，i ∈ N =（1，2，.），其中Δx| t = θ <$x（θ +）− x（θ），x（θ +）= limt → θ+x（t）.李雅普诺夫第二方法被用来作为一种工具，在获得的标准稳定性，渐近稳定性，不稳定的平凡的解决方案。
Abstract The paper is concerned with the stability of the zero solution of the impulsive system dx dt = f t, x , t ≠ θ i x Δx| t = θ i (x) = J i x , i ∈ N = (1, 2,…) , where Δx|t = θ ≔ x(θ + ) − x(θ), x(θ + ) = limt → θ+x(t). The Lyapunov second method is used as a tool in obtaining the criteria for stability, asymptotic stability, and instability of the trivial solution.