  Motivated by networked systems, stochastic control, optimization, and a wide
variety of applications, this work is devoted to systems of switching jump
diffusions. Treating such nonlinear systems, we focus on stability issues.
First asymptotic stability in the large is obtained. Then the study on
exponential p-stability is carried out. Connection between almost surely
exponential stability and exponential p-stability is exploited. Also presented
are smooth-dependence on the initial data. Using the smooth-dependence,
necessary conditions for exponential p-stability are derived. Then criteria for
asymptotic stability in distribution are provided. A couple of examples are
given to illustrate our results.
