  In this paper, we study a wireless networked control system (WNCS) with $N
\ge 2$ sub-systems sharing a common wireless channel. Each sub-system consists
of a plant and a controller and the control message must be delivered from the
controller to the plant through the shared wireless channel. The wireless
channel is unreliable due to interference and fading. As a result, a packet can
be successfully delivered in a slot with a certain probability. A network
scheduling policy determines how to transmit those control messages generated
by such $N$ sub-systems and directly influences the transmission delay of
control messages. We first consider the case that all sub-systems have the same
sampling period. We characterize the stability condition of such a WNCS under
the joint design of the control policy and the network scheduling policy by
means of $2^N$ linear inequalities. We further simplify the stability condition
into only one linear inequality for two special cases: the perfect-channel case
where the wireless channel can successfully deliver a control message with
certainty in each slot, and the symmetric-structure case where all sub-systems
have identical system parameters. We then consider the case that different
sub-systems can have different sampling periods, where we characterize a
sufficient condition for stability.
