以柔性板为对象，开展时滞H∞控制的理论与实验研究．首先给出柔性板的时滞动力学方程；然后利用Lyapunov-Krasovskii泛函和自由权矩阵法，推导了闭环时滞系统渐近稳定的矩阵不等式；进而根据该矩阵不等式采用参数调节法及遗传算法，研究了如下两类控制设计问题：已知控制律求解最大稳定时滞量，已知最大稳定时滞量求解H∞控制律；最后对理论研究成果进行了数值仿真和实验验证．结果显示，获得的H∞控制律能够有效地抑制板的弹性振动，所确定出的保证系统稳定性的时滞区间更接近实际情况．%This paper presents theoretical and experimental studies of H∞ control for a flexible plate with time delay. Firstly, the time-delay dynamic equation of the plate is established. Secondly, a matrix inequality for system asymptotic stability is derived by using the Lyapunov-Krasovskii functional and free-weighting matrix method. Based on the matrix inequality, two control design problems are solved by using the parameter 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 theoretical results. Simulation and experimental results demonstrate that the designed H∞ controller is effective in reducing the plate vibration and the determined maximum time delay guaranteeing the system stability is close to the real time delay of the system.
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