On the incremental form of dissipativity

TL;DR

This paper explores the relationship between dissipativity theory and incremental analysis in nonlinear control, aiming to bridge a theoretical gap and identify new approaches for incremental system analysis.

Contribution

It investigates whether the gap between dissipativity and incremental analysis is fundamental and proposes new avenues to connect these concepts.

Findings

Identifies limitations in current dissipativity theory for incremental analysis

Proposes potential methods to integrate incremental properties into dissipativity framework

Highlights the importance of incremental properties in nonlinear feedback systems

Abstract

Following the seminal work of Zames, the input-output theory of the 70s acknowledged that incremental properties (e.g. incremental gain) are the relevant quantities to study in nonlinear feedback system analysis. Yet, non-incremental analysis has dominated the use of dissipativity theory in nonlinear control from the 80s. Results connecting dissipativity theory and incremental analysis are scattered and progress has been limited. This abstract investigates whether this theoretical gap is of fundamental nature and considers new avenues to circumvent it.