# A Comparison of LPV Gain Scheduling and Control Contraction Metrics for Nonlinear Control

## TL;DR

This paper compares LPV gain scheduling and Control Contraction Metrics (CCMs) for nonlinear control, highlighting CCMs' ability to achieve global stability and performance through an integrated control approach.

## Contribution

It demonstrates that CCM-based control extends gain scheduling by providing global stability and performance guarantees via an exact control realization.

## Key findings

- CCMs achieve global reference-independent stability.
- CCMs integrate local controllers for path-based control.
- Comparison shows CCMs' advantages over traditional LPV gain scheduling.

## Abstract

Gain-scheduled control based on linear parameter-varying (LPV) models derived from local linearizations is a widespread nonlinear technique for tracking time-varying setpoints. Recently, a nonlinear control scheme based on Control Contraction Metrics (CCMs) has been developed to track arbitrary admissible trajectories. This paper presents a comparison study of these two approaches. We show that the CCM based approach is an extended gain-scheduled control scheme which achieves global reference-independent stability and performance through an exact control realization which integrates a series of local LPV controllers on a particular path between the current and reference states.