  In this paper, the feedback stabilization of a linear time-invariant (LTI)
multiple-input multiple-output (MIMO) system cascaded by a linear stochastic
system is studied in the mean-square sense. Here, the linear stochastic system
can model a class of correlated stochastic uncertainties such as channel
uncertainties induced by packet loss and random transmission delays in
networked systems. By proposing a key parameter called coefficient of frequency
variation to characterize the correlation of the stochastic uncertainties, we
present a necessary and sufficient condition of the mean-square stability for
this MIMO stochastic feedback system. After then a necessary and sufficient
condition for the mean-square stabilizability is provided, which reveals a
fundamental limit imposed by the system's unstable poles, nonminimum-phase
(NMP) zeros, relative degrees (input delays), and the coefficient of frequency
variation of the stochastic uncertainties. A numerical example is presented to
illustrate the fundamental constraints in the mean-square stabilizability of
MIMO networked systems with parallel communication channels.
