Stability criteria for singularly perturbed impulsive linear switched systems

We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove that the stability or instability of these auxiliary systems directly determines that of the original system in the regime of small singular perturbation parameters.

💡 Research Summary

The paper investigates a class of singularly perturbed impulsive linear switched systems in which the slow‑fast decomposition of the state variables changes with each switching mode. The system Σε is described by a differential equation Dεk · Ẋ(t)=Λk X(t) on each interval