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

Optimal Control for Discrete-time NCSs with Input Delay and Markovian Packet Losses: Hold-Input Case