# LPV Modeling of Nonlinear Systems: A Multi-Path Feedback Linearization Approach

arXiv: https://arxiv.org/abs/2103.14622 · HTML: https://mlsanity.com/paper/2103.14622/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2021.

## Built on by (most cited first, 1 of 1)

- [PAC bounds of continuous Linear Parameter-Varying systems related to neural ODEs](https://mlsanity.com/paper/2307.03630/) (2023)

## Abstract (arXiv)

This paper introduces a systematic approach to synthesize linear parameter-varying (LPV) representations of nonlinear (NL) systems which are described by input affine state-space (SS) representations. The conversion approach results in LPV-SS representations in the observable canonical form. Based on the relative degree concept, first the SS description of a given NL representation is transformed to a normal form. In the SISO case, all nonlinearities of the original system are embedded into one NL function, which is factorized, based on a proposed algorithm, to construct an LPV representation of the original NL system. The overall procedure yields an LPV model in which the scheduling variable depends on the inputs and outputs of the system and their derivatives, achieving a practically applicable transformation of the model in case of low order derivatives. In addition, if the states of the NL model can be measured or estimated, then a modified procedure is proposed to provide LPV models scheduled by these states. Examples are included to demonstrate both approaches.