Optimal Periodic Control of Discrete-Time LTI Systems

This article tackles the optimal partial output feedback control problem for discrete-time time-invariant systems with quadratic cost. It is shown via the theory of periodic systems and using simple examples that the classical linear time-invariant $\mathcal {H}_{2}$ optimal full-order output feedback controller can be outperformed by a linear periodic full-order output feedback controller. In our opinion, this fact is not available till now in the literature. A new design procedure for the optimal controller is proposed via linear matrix inequality (LMI). The optimal closed-loop cost is evaluated as a function of the period $h$. Illustrative examples are solved, solutions are compared, and consequences are discussed.