Approximate bisimulation for a class of stochastic hybrid systems

We develop a notion of approximate bisimulation for a class of stochastic hybrid systems, namely, the jump linear stochastic systems (JLSS). The idea is based on the construction of the so called stochastic bisimulation function, which quantify the distance between two jump linear stochastic systems. The function is then used to quantify the distance between a given JLSS and its abstraction, and hence quantify the quality of the abstraction. We show that this idea can be applied to simplify safety verification for JLSS. We also show that in the absence of internal disturbances, we can pose the construction of quadratic stochastic bisimulation functions as a tractable linear matrix inequality problem.