# From Dissipativity Theory to Compositional Abstractions of Interconnected Stochastic Hybrid Systems

arXiv: https://arxiv.org/abs/1805.08815 · HTML: https://mlsanity.com/paper/1805.08815/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2018.

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

- [Learning Dissipative Neural Dynamical Systems](https://mlsanity.com/paper/2309.16032/) (2023)

## Abstract (arXiv)

In this work, we derive conditions under which compositional abstractions of networks of stochastic hybrid systems can be constructed using the interconnection topology and joint dissipativity-type properties of subsystems and their abstractions. In the proposed framework, the abstraction, itself a stochastic hybrid system (possibly with a lower dimension), can be used as a substitute of the original system in the controller design process. Moreover, we derive conditions for the construction of abstractions for a class of stochastic hybrid systems involving nonlinearities satisfying an incremental quadratic inequality. In this work, unlike existing results, the stochastic noises and jumps in the concrete subsystem and its abstraction need not to be the same. We provide examples with numerical simulations to illustrate the effectiveness of the proposed dissipativity-type compositional reasoning for interconnected stochastic hybrid systems.