  This paper is concerned with the linear quadratic optimal control problem for
networked system simultaneously with input delay and Markovian dropout.
Different from the results in the literature, we consider the hold-input
strategy, which is much more computationally complicated than zero-input
strategy, but much better in most cases especially in the transition phase.
Necessary and sufficient conditions for the solvability of optimal control
problem over a finite horizon are given by the coupled difference Riccati-type
equations. Moreover, the networked control system is mean-square stability if
and only if the coupled algebraic Riccati-type equations have a particular
solution. The key technique in this paper is to tackle the forward and backward
difference equations, which are more difficult to be dealt with, due to the
adaptability of controller and the temporal correlation caused by simultaneous
input delay and Markovian jump.
