In this paper, the problem of preview tracking control for a class of discrete-time nonlinear Lur’e systems is investigated. To overcome the difficulty arising from the sector nonlinearity, the original system is transformed into a linear parameter varying (LPV) system, and a new auxiliary method is introduced. The difference between the state vector and the auxiliary variable is used instead of the usual difference between system states. At the same time, the tracking error and the previewable future reference information are also considered in order to construct an augmented error system (AES). Then, the preview tracking problem is reduced to a robust control problem. Note that the AES is still an LPV system. Next, a state feedback controller is developed to ensure that the closed-loop system is asymptotically stable with H∞ guaranteed cost performance. Based on this, a preview controller for the original system is proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the controller.
Semi-global incremental input-to-state stability of discrete-time Lur’e systems
