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tracking control; preview control; nonlinear Lur'e system; linear matrix inequality
In this paper, the tracking control problem for a class of discrete-time nonlinear Lur'e systems with time-varying delays and external disturbances is studied via a preview control method. First, a novel translation approach is introduced to construct the augmented error system for Lur'e systems. The output tracking problem is thereby transformed into a guaranteed cost $H_\infty$ controller design problem. To produce an integral control action that can eliminate the static error, a discrete integrator is included. Next, a memory state feedback controller is developed, and the sufficient conditions for asymptotic stability and guaranteed cost $H_\infty$ performance of the closed-loop system are established by applying a suitable Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique. Based on this, the tracking control scheme with preview action for the original system is presented. Finally, the effectiveness of our proposed control method is illustrated via a numerical example.
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