  This paper provides a new unified framework for second-moment stability of
discrete-time linear systems with stochastic dynamics. Relations of notions of
second-moment stability are studied for the systems with general stochastic
dynamics, and associated Lyapunov inequalities are derived. Any type of
stochastic process can be dealt with as a special case in our framework for
determining system dynamics, and our results together with assumptions (i.e.,
restrictions) on the process immediately lead us to stability conditions for
the corresponding special stochastic systems. As a demonstration of usefulness
of such a framework, three selected applications are also provided.
