  The mean square stabilization problem for discrete-time networked control
systems (NCSs) is investigated in this article. What the difference from most
previous works is that input delay and packet losses occur simultaneously in
the communication channel, moreover, the data packet dropout is modeled as a
time-homogeneous Markov process which will bring some difficulties in solving
the problem due to the temporal correlation. The contributions in this paper
can be summarized as two points. Firstly, the equivalence condition for the
solvability of linear quadratic optimal problem in finite horizon subject to
the discrete-time NCSs is expressed by solving the forward and backward
stochastic difference equations (FBSDEs-M) which is derived from the maximum
principle involving Markov jump and delay. Secondly, under basic assumption,
the necessary and sufficient condition of mean square stabilization is given by
the solutions to the coupled algebraic Riccati equations with Markov jump
(CAREs-M). To our best knowledge, the problems studied in this paper are new
because most previous works mainly discussed the case of only delay or packet
dropout in NCSs.
