Descriptor Impulsive Systems: Consistency, Admissibility and Impulse-Free Behavior

This preprint presents a unified theoretical framework for descriptor impulsive dynamical systems by integrating geometric consistency, descriptor admissibility, and structural impulse-free behavior. The framework introduces the concept of the admissible descriptor manifold and formulates general conditions ensuring that impulsive reset mappings preserve descriptor consistency while the underlying descriptor dynamics remain free of hidden impulsive modes. The work combines geometric and structural descriptor-system viewpoints and includes illustrative low-dimensional examples, numerical simulations, conceptual diagrams, and reproducibility code. The deposited archive contains the final manuscript, Figures 1–17, editable figure sources, and Python scripts reproducing Figures 7, 8, 9, 10, and 12. The reference list is organized thematically to reflect the historical and early conceptual development of the singular, descriptor, and impulsive-system theories that form the theoretical basis of the proposed framework.