A unified analytical framework for joint design of communication and control (JDCC) is proposed. Within this framework, communication transmission delay and steady-state control variance are derived as the two fundamental JDCC performance metrics. The Pareto boundary is then established to characterize the optimal communication-control trade-off in JDCC systems. To further obtain closed-form expressions, their performance regions are derived under maximum-ratio transmission (MRT) and zero-forcing (ZF) beamforming. For system reliability evaluation, the communication-only and control-only outage probabilities are first derived. Based on these, the JDCC outage probability is defined to quantify the probability that the communication-delay and control-error requirements cannot be simultaneously satisfied. Its analytical expressions are then derived under both MRT and ZF schemes. Finally, numerical results validate the theoretical results and reveal that: (1) the Pareto boundary characterizes the trade-off frontier and performance limit of JDCC systems and (2) the JDCC reliability is jointly determined by the uplink-downlink closed-loop control and its coupling with communication.

翻译：针对通信与控制联合设计（JDCC）问题，本文提出统一分析框架。在该框架内，将通信传输时延与稳态控制方差确立为两项基本JDCC性能指标，进而构建帕累托边界以表征JDCC系统中最优通信-控制权衡关系。为获得闭式表达式，进一步推导了最大比传输（MRT）与迫零（ZF）波束赋形下的性能区域。在系统可靠性评估方面，首先推导了纯通信中断概率与纯控制中断概率，并据此定义JDCC中断概率以量化通信时延与控制误差需求无法同时满足的概率，随后给出了MRT与ZF两种方案下JDCC中断概率的解析表达式。最后，数值结果验证了理论分析并揭示：（1）帕累托边界刻画了JDCC系统的权衡前沿与性能极限；（2）JDCC可靠性由上下行闭环控制及其与通信系统的耦合共同决定。