Abstract
This paper investigates the exponential stability problem for a class of singularly perturbed impulsive systems in which the flow dynamics is unstable and is affected at discrete time instants by impulses that have both destabilizing and stabilizing effects. More precisely the impulses have stabilizing effects on the slow variables but destabilizing effects on the fast ones. Thus, a first contribution of our work is related to stability analysis of singularly perturbed impulsive systems in the case when neither the flow dynamics nor the impulsive one is stable. In order to take full advantage of the jump matrix structure and its stabilizing effects on the slow dynamics, we introduce a new impulse-dependent vector Lyapunov function. This function allows us to better describe the behavior between two consecutive impulses as well as the jumps at impulse instants. Several numerically tractable criteria for stability of singularly perturbed impulsive systems are established based on vector comparison principle. Additionally, upper bounds on the singular perturbation parameter are derived. Finally, the validity of our results is verified by two numerical examples.
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