Optimal Discretization of Analog Filters via Sampled-Data H-infinity Control Theory

TL;DR

This paper introduces a method for optimally discretizing analog filters using sampled-data H-infinity control theory, minimizing approximation error while ensuring stability, applicable to multirate systems.

Contribution

It formulates the discretization as an H-infinity norm minimization problem and extends the approach to multirate systems, providing a systematic optimal discretization framework.

Findings

Numerical examples demonstrate the effectiveness of the proposed method.

The approach achieves minimal error in discretization while maintaining stability.

Extension to multirate systems broadens applicability.

Abstract

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.