High control performances cannot be obtained by most of the existing looper-tension control approaches through only considering controller designs based on continuous-time models,which cannot meet the requirements of modern computer control systems with high control accuracy.In order to solve the above problems,a state feedback H∞control method based on a discrete-time model for looper-tension control systems in hot rolling mills is presented.The considered system is approximated by a discrete-time looper-tension control system model.Based on a Lyapunov functional method,a state feedback H∞control law is developed which makes the closed-loop system asymptotically stable with guaranteed H∞performance.The controller gains are obtained by solving a set of linear matrix inequalities(LMIs).In contrast to the existing results,the proposed approach can obtain good H∞performance and effectively reduce external disturbances.The strip tension is also less affected by the change of looper angel,so good control performances can be obtained.Moreover,this control scheme is easy to implement,and can be applied to other linear systems.A simulation example with practical parameters is provided to illustrate the effectiveness of the developed method. High control performances can not be obtained by most of the existing looper-tension control approaches through only considering controller designs based on continuous-time models, which can not meet the requirements of modern computer control systems with high control accuracy. , a state feedback H∞control method based on a discrete-time model for looper-tension control systems in hot rolling mills is presented. The considered system is approximated by a discrete-time looper-tension control system model. Based on a Lyapunov functional method, a state feedback H∞control law is developed which makes the closed-loop system asymptotically stable with guaranteed H∞performance.The controller gains are solved by a set of linear matrix inequalities (LMIs) .In contrast to the existing results, the proposed approach can obtain good H∞performance and effectively reduce external disturbances.The strip tension is also less affected by the change of looper angel, so good control performances can be obtained. Moreover, this control scheme is easy to implement, and can be applied to other linear systems. A simulation example with practical parameters is provided to illustrate the effectiveness of the developed method.