# Metrization and Simulation of Controlled Hybrid Systems

arXiv: https://arxiv.org/abs/1302.4402 · HTML: https://mlsanity.com/paper/1302.4402/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2013.

## Built on by (most cited first, 1 of 1)

- [CHyLL: Learning Continuous Neural Representations of Hybrid Systems](https://mlsanity.com/paper/2512.10117/) (2025)

## Abstract (arXiv)

The study of controlled hybrid systems requires practical tools for approximation and comparison of system behaviors. Existing approaches to these problems impose undue restrictions on the system's continuous and discrete dynamics. Metrization and simulation of controlled hybrid systems is considered here in a unified framework by constructing a state space metric. The metric is applied to develop a numerical simulation algorithm that converges uniformly, with a known rate of convergence, to orbitally stable executions of controlled hybrid systems, up to and including Zeno events. Benchmark hybrid phenomena illustrate the utility of the proposed tools.