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On Stability Condition of Wireless Networked Control Systems under Joint Design of Control Policy and Network Scheduling Policy
In this paper, we study a wireless networked control system (WNCS) with 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 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 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