Design of discrete $\mathcal H_2$-optimal reduced-order controllers

Consideration was given to the design of discrete dynamic reduced-order controllers minimizing the $\mathcal H_2$-norm of the transfer matrix of a closed-loop system. The problem of reducing the controller order is related to the solution of the singular problem of filtration (no measurement noise) and control (no control at the controlled output). Using the well-known structures of controllers based on the corresponding minimum-order observers, these problems were shown to be reducible to the solution of two Riccati equations of which one is of a reduced order. Peculiarities of solution that are characteristic of the digital controllers and caused by the allowance for astatism and presence of control delays were examined. An example of an $\mathcal H_2$-optimal reduced-order controller was presented to illustrate the results obtained.