  This work studies mean-square stabilizability via output feedback for a
networked linear time invariant (LTI) feedback system with a non-minimum phase
plant. In the feedback system, the control signals are transmitted to the plant
over a set of parallel communication channels with possible packet dropout. Our
goal is to analytically describe intrinsic constraints among channel packet
dropout probabilities and the plant's characteristics, such as unstable poles,
non-minimum phase zeros in the mean-square stabilizability of the system. It
turns out that this is a very hard problem. Here, we focus on the case in which
the plant has relative degree one and each non-minimum zero of the plant is
only associated with one of control input channels. Then, the admissible region
of packet dropout probabilities in the mean-square stabilizability of the
system is obtained. Moreover, a set of hyper-rectangles in this region is
presented in terms of the plant's non-minimum phase zeros, unstable poles and
Wonham decomposition forms which is related to the structure of controllable
subspace of the plant. When the non-minimum phase zeros are void, it is found
that the supremum of packet dropout probabilities' product in the admissible
region is determined by the product of plant's unstable poles only. A numerical
example is presented to illustrate the fundamental constraints in the
mean-square stabilizability of the networked system.
