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H∞ Preview Control of A Class of Uncertain Discrete‐Time Systems

This paper investigates the problem of H∞ preview tracking control with robust performance for uncertain discrete‐time systems. In order to avoid applying the difference operator to the time‐varying matrix, by taking advantage of the difference between the system state variables, input variables, and the corresponding auxiliary variables, instead of the usual difference between system states, an augmented error system including previewed information is constructed, which converts the tracking problem into a regulator problem. A sufficient condition based on the free‐weighting matrices technique and the Lyapunov stability theory is derived for the robust asymptotic stability of uncertain systems. Moreover, a state feedback control law with preview action design method is obtained via the linear matrix inequality approach. Based on these, a state observer for preview control systems is formulated. Previewable reference signals are fully utilized through reformulation of the output equation while designing the state observer. The proposed construction method of augmented error system is applicable to uncertain discrete‐time systems in which the uncertainties are general. Also an integrator is introduced to ensure the closed‐loop system tracking performance with no static error. The numerical results also show the effectiveness of the preview control law for uncertain systems in the paper.