Parameter-dependent preview control with robust tracking performance

The problem of static output feedback preview tracking control is proposed for a class of polytopic uncertain discrete-time systems by combining parameter-dependent Lyapunov function method with linear matrix inequality (LMI) technique. First, the error system method of preview control theory is adopted and the difference operator is introduced, and then an augmented error system including previewed information is constructed, which transforms a tracking problem into a regulation problem. Then, a previewable reference signal is fully utilised through reformulation of the output equation for the derived augmented error system while considering the output feedback. Sufficient conditions for designing a robust static feedback preview controller are given in terms of solutions to a set of LMIs. Based on the criterion, a static output feedback controller with preview action is designed such that the output can asymptotically track the reference signal. Finally, the numerical simulation examples also illustrate the superiority of the desired preview controller for the uncertain system in the study.