Constructing Dynamic Feedback Linearizable Discretizations

TL;DR

This paper introduces a method to construct discretization schemes for nonlinear systems that preserve feedback linearizability, extending previous work from static to dynamic feedback linearization, applicable to a broad class of systems.

Contribution

It presents a novel approach to discretize nonlinear systems while maintaining feedback linearizability, applicable to both endogenous and exogenous feedback types.

Findings

Constructed first-order accurate discretization schemes that are feedback linearizable.

Extended previous static feedback linearization methods to dynamic feedback linearization.

Applicable to a broad class of nonlinear systems, including control affine forms.

Abstract

Dynamic feedback linearization-based methods allow us to design control algorithms for a fairly large class of nonlinear systems in continuous time. However, this feature does not extend to their sampled counterparts, i.e., for a given dynamically feedback linearizable continuous time system, its numerical discretization may fail to be so. In this article, we present a way to construct discretization schemes (accurate up to first order) that result in schemes that are feedback linearizable. This result is an extension of our previous work, where we had considered only static feedback linearizable systems. The result presented here applies to a fairly general class of nonlinear systems, in particular, our analysis applies to both endogenous and exogenous types of feedback. While the results in this article are presented on a control affine form of nonlinear systems, they can be readily modified to general nonlinear systems.