Abstract
The paper studies global asymptotic stability property of the trivial solution to nonlinear impulsive differential equations. Robustness of the global asymptotic stability with respect to the perturbations of the moments of jumps is investigated. Less conservative estimates on the admissible magnitude of perturbations preserving stability compared to the existing ones in the literature are proposed. A relation between stability properties of the perturbed and unperturbed systems is studied. Finally, utilizing Wintner–Conti theorem, we present two new Lyapunov-like theorems ensuring the global asymptotic stability of the impulsive system with unstable continuous dynamics that is being stabilized by impulsive jumps and discuss their relation to the previously known results.
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