Linear Parameter-Varying Control of Nonlinear Systems based on Incremental Stability

TL;DR

This paper introduces an LPV control synthesis method that guarantees incremental stability and performance of nonlinear systems, improving tracking and disturbance rejection over traditional $ ext{L}_2$-based approaches.

Contribution

The paper presents a novel LPV synthesis approach that ensures incremental stability and performance for nonlinear systems with reference and disturbance rejection.

Findings

Proposed method guarantees incremental stability and performance.

Simulation shows improved tracking and disturbance rejection.

Compared to traditional $ ext{L}_2$-based LPV control.

Abstract

The Linear Parameter-Varying (LPV) framework has long been used to guarantee performance and stability requirements of nonlinear (NL) systems mainly through the $\mathcal{L}_2$-gain concept. However, recent research has pointed out that current $\mathcal{L}_2$-gain based LPV synthesis methods can fail to guarantee these requirements if stabilization of a non-zero operating condition (e.g. reference tracking, constant disturbance rejection, etc.) is required. In this paper, an LPV based synthesis method is proposed which is able to guarantee incremental performance and stability of an NL system even with reference and disturbance rejection objectives. The developed approach and the current $\mathcal{L}_2$ LPV synthesis method are compared in a simulation study of the position control problem of a Duffing oscillator, showing performance improvements of the proposed method compared to the current $\mathcal{L}_2$-based approach for tracking and disturbance rejection.