On differentially dissipative dynamical systems

TL;DR

This paper introduces differential dissipativity, extending classical dissipativity to tangent bundles, and explores its implications for incremental stability and differential passivity in interconnected systems.

Contribution

It extends dissipativity theory to differential dissipativity, linking it to incremental stability and differential passivity, with applications to electrical systems.

Findings

Differential dissipativity generalizes classical dissipativity.

Interconnection of differentially passive systems remains differentially passive.

Preliminary examples demonstrate differential passivity in electrical systems.

Abstract

Dissipativity is an essential concept of systems theory. The paper provides an extension of dissipativity, named differential dissipativity, by lifting storage functions and supply rates to the tangent bundle. Differential dissipativity is connected to incremental stability in the same way as dissipativity is connected to stability. It leads to a natural formulation of differential passivity when restricting to quadratic supply rates. The paper also shows that the interconnection of differentially passive systems is differentially passive, and provides preliminary examples of differentially passive electrical systems.