Output feedback preview control for periodic systems

In this paper, the static output periodic preview control problem of discrete-time periodic systems (D-TPSs) is proposed. First, an augmented error periodic system (AEPS) is derived by introducing auxiliary variables related to the system state and input. Consequently, the static output periodic preview control problem is transformed into a stabilization problem. Second, sufficient conditions are derived to ensure asymptotic stability, and these conditions are extended to the D-TPSs with disturbance. Moreover, the corresponding solvability condition for the design of the static output periodic preview control laws is proposed using linear matrix inequality (LMI). Finally, a numerical example is used to illustrate the effectiveness of the results.