  A Network Control System (NCS) consists of control components that interact
with the plant over a shared network. The system dynamics of a NCS could be
subject to noise arising from randomness in the times at which the data is
transmitted over the network, corruption of the transmitted data by the
communication network, and external disturbances that might affect the plant. A
question of interest is to understand how the statistics of the data
transmission times affects the system dynamics, and under what conditions the
system is stable. Another related issue is designing a controller that meets
desired performance specifications (e.g., a specific mean and variance of the
system state). Here, we consider a minimal NCS that consists of a plant and a
controller, and it is subject to random transmission times, channel corruption
and external disturbances. We derive exact dynamics of the first two moments of
the system, and use them to derive the stability conditions of the system. We
further design a control law that steers the system to a desired mean and
variance. Finally, we demonstrate our results using different examples, and
show that under some specific conditions, randomness in the data transmission
times can even reduce the variability contributed from disturbance.
