H_∞ optimal preview control with robust tracking performance

A robust H_∞ preview control problem is proposed for a class of uncertain discrete-time systems. A new method is derived to construct an augmented error system,avoiding applying the difference operator to the time-varying matrix,and simplify the augmented error system. Then for the augmented error system of the uncertain system,the problem of guaranteed cost robust H_∞ control is considered via a state feedback with integral and preview actions. The sufficient condition for the existence of the robust H_∞ controller and H_∞ state feedback controller design methods are presented. The condition can be realized by solving a linear matrix inequality optimization problem. By putting the controller obtained into the original system,we can get the preview controller. Moreover,introducing an integrator makes the closed-loop system robustly track the reference signal without steady-state error. The effectiveness of the proposed method is shown by numerical simulation.