Summary This paper considers the preview tracking control problem of polytopic uncertain discrete‐time systems with a time‐varying delay subject to a previewable reference signal. First, a model transformation is employed and a discrete‐time system with a time‐invariant delay and an external disturbance is obtained. The difference operator method can be extended to derive an augmented error system that includes future information on the reference signal. Then, a previewable reference signal is fully utilized through reformulation of the output equation while considering the output feedback. Based on the small gain theorem, a static output feedback controller with preview actions is designed such that the output can asymptotically track the reference signal. Finally, numerical simulation examples also illustrate the superiority of the desired preview controller for the uncertain system in the paper.

In this paper, the stabilization analysis problem of a bi‐directional coupled ODE‐PDE system is proposed. The spatially varying coefficient and the intermediate point interaction between the subsystems makes the coupled system more representative. An invertible infinite‐dimensional backstepping transformation is introducted to bring the original system into an exponentially stable target system. By employing the backstepping method, the kernel functions in the transformations are worked out under some assumptions of the spatially varying coefficient. Then, an explicit state‐feedback law is designed and the exponential stability of the transformed closed‐loop system has been also discussed. Finally, numerical simulation is provided to illustrate the effectiveness of the proposed design.