ampling signals of the plant state to the base station (BS), the remote controller in the BS processing the sampling signals, and then the BS send- ing the calculated control command signals to the M corresponding static plants. With the control process continuing, the state of each plant will converge to a preset value. Note that all the notations to be used throughout the chapter for communi- cation subsystem and control subsystem are summarized in Tables 14.1 and 14.2, respectively. 14.2.1 Wireless Control Model In this section, we present the real-time wireless control model considering communication time delay and reliability. Except for the inherent control parameters, e.g. the mass and the speed of the plant, the main coefficients that contribute to control performance include sampling period at the sensor and communication QoS [17]. Since we focus on the con- trol convergence rate requirement and communication QoS, a constant sampling period is adopted. Then, the continuous control function for the m-th plant is given by a linear differential equation as [25] dxm(t) = AmXm(t)dt + BmUm(t)dt + dnm(t), (14.1) where Xm(t) is the state of the m-th plant, Um(t) is the control input, and nm(t) is the distur- bance caused by AWGN with zero mean and variance Rm. In addition, Am and Bm represent the system parameter matrices. To illustrate the system parameters Am m and Bm, m' we consider a controlled inverted pendulum system as shown in Figure 14.2. 14.2 System Model with Latency and Reliability Constraints Table 14.1 Summary of notations for communication subsystem Bandwidth of each subcarrier Coverage radius of the BS Shannon capacity of the m-th sensor at Maximum transmission time delay time index n Path loss of the m-th sensor Time resource of the uplink for the m-th sensor Small scale fading for the m-th sensor Channel dispersion for the m-th sensor Total available number of subcarriers Indicator for packet loss Number of subcarriers for the m-th Received SNR of the m-th sensor sensor Distance between the m-t