Optimal discretization of analog filters via sampled-data H∞ control theory

In this article, we propose optimal discretization of analog filters (or controllers) based on the theory of sampled-data H^∞ control. We formulate the discretization problem as minimization of the H^∞ 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^∞ 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.