A novel power and rate control system model for wireless communication networks is presented, which includes uncertainties, input constraints, and time-varying delays in both state and control input. A robust delay-dependent model predictive power and rate control method is proposed, and the state feedback control law is obtained by solving an optimization problem that is derived by using linear matrix inequality (LMI) techniques. Simulation results are given to illustrate the effectiveness of the proposed method.A challenge issue in power and rate control is to maintain robustness to time delay [9,10,12]. To compensate for the effect of time delay, power and rate control algorithms have been presented by using a multiple-mode Smith prediction filter in [7] and by using a high order model in [9,10]. From a system-theoretic perspective, a power and rate control algorithm for wireless networks with state delay was presented in [12], which minimized the bound on the error variance between the desired and actual SIR. However, almost all existing power and rate control methods are limited to consider known and constant time delay. Unfortunately, the time delay is often unknown and even time-varying in real network environments.In the previous work, we presented power and rate control algorithms for wireless networks with time-varying state delay via adaptive control technique [13] and via robust ∞ control approach [14]. However, as in [12], the time delay only in rate control was considered, while the time delay in power control was not considered. In fact, the power control is more sensitive to time delay than the rate control. Additionally, only the state time delay was considered in [12][13][14], but the input delay was not considered. To the best knowledge of the authors, research on power and rate control for wireless communication networks with time-varying delays in both state and control input has not been investigated, which is another motivation of this paper.Another challenge issue in power and rate control is to maintain robustness to uncertainties and input constraints. It is well known that robust control with linear matrix inequality (LMI) is a powerful technique to cope with uncertainties, and model predictive control (MPC) has strong ability to handle input constraints [15,16]. Therefore, a robust MPC with LMI can be extended to power and rate control for wireless communication networks with uncertainties and input constraints, which is the third motivation of this paper.The main contributions of this paper are as follows.(1) In the control theoretic framework, a novel power and rate control system model is presented, which includes uncertainties, input constraints, and time-varying state and input delays in both rate control and power control. (2) A robust model predictive power and rate control method is presented for wireless communication networks with uncertainties, input constraints, and time-varying state and input delays. The state feedback control law is obtained by solving an optimization pr...