This paper is concerned with the linear–quadratic optimal control problem for networked systems simultaneously with input delay and Markovian packet losses under hold-input compensation strategy, which is different from the literature. Necessary and sufficient conditions for the solvability of optimal control problem over a finite horizon are given by coupled difference Riccati-type equations. Moreover, the networked control system is mean-square stability if and only if coupled algebraic Riccati-type equations have a particular solution. Due to input delay and Markovian packet dropout, it leads to the failure of the separation principle, which is a fundamental obstacle. The key technique in this paper is to tackle forward and backward difference equations by decoupling.

本文关注的是在保持输入补偿策略下同时具有输入延迟和马尔可夫丢包的网络系统的线性-二次最优控制问题，这与文献不同。耦合差分 Riccati 型方程给出了有限范围内最优控制问题可解性的充要条件。此外，当且仅当耦合代数 Riccati 型方程具有特定解时，网络控制系统才具有均方稳定性。由于输入延迟和马尔可夫丢包，导致分离原理失效，这是一个根本性的障碍。本文的关键技术是通过解耦来处理前向和后向差分方程。