Discretisation of continuous-time linear dynamical model with the Loewner interpolation framework

TL;DR

This paper introduces a novel interpolation-based method for discretising continuous-time LTI models using the Loewner framework, enabling flexible accuracy and stability control with improved matching of magnitude and phase.

Contribution

It proposes a new discretisation approach combining Loewner interpolation with stable subspace projection, offering better accuracy and flexibility than traditional methods.

Findings

Outperforms ZOH and Tustin in magnitude and phase matching

Allows higher-order models for increased accuracy

Demonstrates efficiency through numerical examples

Abstract

An interpolation method for discretising continuous-time Linear Time Invariant (LTI) models is proposed in this paper. It consists first in using the Loewner interpolation framework on a specific set of frequency data and secondly to project the resulting model onto a stable subspace. The order of the discretised model may be chosen larger than the initial one thus allowing for trading complexity for accuracy if needed. Numerical examples highlight the efficiency of the method at preserving a satisfactory matching both in magnitude and phase in comparison to standard discretisation methods like ZOH or Tustin.