31), we can obtain the relationship between the control requirement on the con- trol convergence rate Pm and communication reliability requirement Pr{am,n = 1}. Here, the lower bound of the communication reliability decreases monotonically with Pm. This is reasonable since the plant state updates smoothly when Pm is small, which leads to good control performance [16]. In summary, small Pm means good control performance and needs high communication reliability to maintain the control performance. On the con- trary, large Pm means loss in control performance and does not need high communication reliability to maintain the control performance. Furthermore, from (14.10) and (14.31), we can infer that the proposed relationship also works in the scenario where there is no trans- mission time delay, in a straightforward manner. (14.32) yERme-mey represent the supremum of the right-hand term in (14.31). According to [34, 35], we can obtain the optimal cm. Based on the above discussion, we can obtain the following theorem about the relation- ship between control and communication. Theorem 14.1 In real-time wireless control systems, communication reliability is actually determined by the control performance constrained by the requirement of control convergence 14.4 Optimal Resource Allocation for The Proposed Co-Design rate, rather than the suggested reliability in communications, i.e. being bounded Eth. Their relationship can be expressed as Pr{am.n=1}>cm. (14.33) Based on Theorem 14.1, we can obtain the following property. Property 14.1 According to the relationship between the control performance constraint C* and the reliability requirement 1 - Eth in - URLLC QoS, the actual resource consump- tion for URLLC in real-time wireless control system can be divided into the following three cases. Case A: When cm>1-Eth, - the actual resource consumption is higher than the bound in the traditional URLLC resource allocation. Case B: When Cm=1-Eth, the actual resource consumption is equal to the bound in the traditional URLLC res