Robust H∞ control of the Discrete-time Uncertain Systems with Time-Delay based on LMI

Based on LMI and proper Lyapunov functions, under the assumption that the uncertainty is norm bounded and the states of the system are available, H_∞ stated feedback controllers can be obtained by solving the corresponding LMI. This approach is proved that can make the closed-loop systems asymptotically stable, meanwhile, the H_∞ norm of the transfer function from the disturbance to the controlled output is reduced to a given constant. At last, a numerical example is presented to illustrate the validity of this approach.