Design of a robust H ∞ preview controller for a class of uncertain discrete-time systems

The robust preview tracking control problem of uncertain discrete-time systems satisfying matching conditions is considered. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to derive an augmented error system that includes the future information on the reference signal and disturbance signal to transform the tracking problem into a regulator problem. Then, a robust preview controller of the augmented error system is proposed by integrating Lyapunov stability theory and LMI approach. Research shows that the preview controller gain matrix can be determined by solving a LMI. The proposed robust preview controller in this paper cannot only guarantee the asymptotic stability of the closed-loop system, but also enhance the interference rejection properties. An integrator is applied to make sure that the output tracks the reference signal with no static error. The numerical simulation example also illustrates the effectiveness of the results presented in the paper.