  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.
