Discretization of Linear Systems using the Matrix Exponential

TL;DR

This paper introduces a straightforward method for discretizing continuous-time linear systems by leveraging a single matrix exponential, simplifying the process of converting continuous models into discrete form.

Contribution

It proposes a novel, unified approach for discretizing system matrices, including dynamics, input, and noise, using matrix exponential, reducing computational complexity.

Findings

Simplifies the discretization process of linear systems.

Reduces computational effort compared to traditional methods.

Applicable to a wide range of continuous-time linear models.

Abstract

Discretizing continuous-time linear systems typically requires numerical integration. This document presents a convenient method for discretizing the dynamics, input, and process noise state-space matrices of a continuous-time linear system using a single matrix exponential.