# Tikhonov Theorem for Differential Equations with Singular Impulses

## TL;DR

This paper extends the Tikhonov theorem to impulsive differential equations with singular impulses, providing new theoretical results and illustrative simulations for such complex systems.

## Contribution

It introduces a novel approach to impulsive systems with singular impulses, expanding the classical Tikhonov theorem to this new class of problems.

## Key findings

- Established conditions for stability of singular impulsive systems
- Proved theorems using Lyapunov second method
- Provided illustrative examples with simulations

## Abstract

The paper considers impulsive systems with singularities. The main novelty of the present research is that impulses (impulsive functions) are singular. This is beside singularity of differential equations. The Lyapunov second method is applied to proof the main theorems. Illustrative examples with simulations are given to support the theoretical results.