Abstract: This paper presents theoretical and experimental studiesof H∞ control for a flexible plate with time delay. Firstly, thetime-delay dynamic equation of the plate is established. Secondly, a matrixinequality for system asymptotic stability is derived by using theLyapunov-Krasovskii functional and free-weighting matrix method. Based onthe matrix inequality, two control design problems are solved by using theparameter adjustment method and genetic algorithm: (1) H∞controller design with known maximum time delay of the system; (2)determination of maximum time delay with known controller. Finally,simulation and experiments are carried out to verify the theoreticalresults. Simulation and experimental results demonstrate that the designedH∞ controller is effective in reducing the plate vibration and thedetermined maximum time delay guaranteeing the system stability is close tothe real time delay of the system.