Abstract: In this paper, the closed-loop performances of predictive control systems for a class of industrial processes are quantitatively analysed. Based on the Internal Model Control (IMC) structure and the minimal form of the controller in the Generalized Dynamic Matrix Control (GDMC) systems, the closed-loop transfer functions of predictive control for typical first order plants with time delay are introduced. The analytical relationships between the main design parameters and the closed-loop dynamics as well as the disturbance rejection time are given and three theorems on closed-loop robustness are presented. Some search algorithms are proposed to find the admissible ranges for gain or time delay mismatches. The new results in the paper provide theoretical foundations: for analysing and designing predictive control systems.