  In this article, we propose optimal discretization of analog filters (or
controllers) based on the theory of sampled-data H-infinity control. We
formulate the discretization problem as minimization of the H-infinity norm of
the error system between a (delayed) target analog filter and a digital system
including an ideal sampler, a zero-order hold, and a digital filter. The
problem is reduced to discrete-time H-infinity optimization via the fast
sample/hold approximation method. We also extend the proposed method to
multirate systems. Feedback controller discretization by the proposed method is
discussed with respect to stability. Numerical examples show the effectiveness
of the proposed method.
