A Lagrange subspace approach to dissipation inequalities

TL;DR

This paper extends dissipation inequalities from storage functions to Lagrange subspaces, introducing a Hamiltonian lift for DAE systems, which broadens the theoretical framework for passivity analysis.

Contribution

It generalizes dissipation inequalities to Lagrange subspaces and introduces the Hamiltonian lift for DAE systems, expanding passivity analysis methods.

Findings

Extended classical factorization for passive systems.

Introduced Hamiltonian lift for DAE systems.

Generalized dissipation inequalities to Lagrange subspaces.

Abstract

The standard dissipation inequality for passivity is extended from storage functions to general Lagrange subspaces. This is shown to have some interesting consequences. A classical factorization result for passive systems is extended to this generalized case, making use of the newly defined concept of the Hamiltonian lift of a DAE system.