Mathematical modeling reveals differences between consistency-preserving and consistency-violating resets in RLC circuits, indicating how algebraic constraints dictate physically admissible states.
This preprint presents a descriptor impulsive formulation of an electrical RLC circuit as a physical application of consistency preservation in impulsive dynamical systems. The circuit is modeled using singular, reduced-order regular, impulsive-system (IS), and descriptor impulsive system (DIS) representations. The study investigates consistency-preserving and consistency-violating reset mappings with respect to the algebraic circuit constraint imposed by Ohm’s law. Numerical simulations, constraint-residual analysis, and geometric representations are used to distinguish physically admissible from inadmissible post-reset states. The deposited archive contains the final manuscript, Figures 1–5, Python scripts reproducing all figures, generated outputs, a README file, and software requirements. This application builds on the theoretical framework developed in: N. A. Kablar, “Descriptor Impulsive Systems: Consistency, Admissibility and Impulse-Free Behavior,” Zenodo, 2026, DOI: 10.5281/zenodo.22030444.
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Nataša A. Kablar (2026) studied this question.
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