  This paper deals with Networked Control Systems (NCSs) whose shared networks
have limited communication capacity and are prone to data losses. We assume
that among (N) plants, only (M < N) plants can communicate with their
controllers at any time instant. In addition, a control input, at any time
instant, is lost in a channel with a probability (p). Our contributions are
threefold. First, we identify necessary and sufficient conditions on the
open-loop and closed-loop dynamics of the plants that ensure existence of
purely time-dependent periodic scheduling sequences under which stability of
each plant is preserved for all admissible data loss signals. Second, given the
open-loop and closed-loop dynamics of the plants, relevant parameters of the
shared network and a period for the scheduling sequence, we present an
algorithm that verifies our stability conditions and if satisfied, designs
stabilizing scheduling sequences. Otherwise, the algorithm reports
non-existence of a stabilizing periodic scheduling sequence with the given
period and stability margins. Third, given the plant matrices, the parameters
of the network and a period for the scheduling sequence, we present an
algorithm that designs static state-feedback controllers such that our
stability conditions are satisfied. The main apparatus for our analysis is a
switched systems representation of the individual plants in an NCS whose
switching signals are time-inhomogeneous Markov chains. Our stability
conditions rely on the existence of sets of symmetric and positive definite
matrices that satisfy certain (in)equalities.
