This collaborative project studies dynamical systems characterized by a combination of hybrid and probabilistic behavior. Hybrid behavior is characterized by discrete switching between system modes and continuous evolution within a mode. Such systems frequently arise in a wide range of applications, from power electronics and communication networks to economics and biology. In this research, a new modeling framework for such systems is developed, which supports external variables, compositional reasoning, and nondeterministic as well as probabilistic transitions. New stability criteria for such probabilistic hybrid systems are obtained. In contrast with existing results, they are formulated in terms of two independent components: a family of Lyapunov functions (one for each continuous mode) and a slow-switching condition of an average-dwell-time type. This modularity has the benefit of decoupling the search for Lyapunov functions from the verification of the desired properties of the discrete dynamics. The latter task is the focus of the project, and is treated using two complementary methods: one based on proving an invariant property, and another based on solving an optimization problem. These theoretical results are supported by development of new software tools.
