ABSTRACT
While impressive progress has been made so far in the study of hybrid systems, a majority of the efforts focus exclusively on deterministic hybrid systems, which are not suitable for modeling practical systems with inherent uncertainty. For example, the trajectory of an aircraft is subject to the perturbations of wind [6], the traffic in a computer network may fluctuate and components may break down at random intervals, and stochastic noises exist in the genetic networks regulating the cells [20] as discussed in Chapter 9 of this volume. To model these systems, it is imperative
to introduce the notion of stochastic hybrid systems, namely, hybrid systems with stochastic continuous dynamics governed by stochastic differential equations and with random discrete mode transitions governed by Markov chains. These are an instance of the stochastic differential equations on hybrid state spaces discussed in Chapter 2 of this volume.
