Incremental stability analysis of stochastic hybrid systems

In this paper, we study the incremental stability of stochastic hybrid systems, based on the contraction theory, and derive sufficient conditions of global stability for such systems. As a special case, the conditions to ensure the second moment exponential stability which is also called exponential stability in the mean square of stochastic hybrid systems are obtained. The theoretical results in this paper extend previous works from deterministic or stochastic systems to general stochastic hybrid systems, which can be applied to qualitative and quantitative analysis of many physical and biological phenomena. An illustrative example is given to show the effectiveness of our results.