Contraction Theory and Differential Passivity in the port-Hamiltonian formalism

Mario Spirito (1, 2) , Bernhard Maschke (1) , Yann Le Gorrec (3)

1 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique
2 UCBL - Université Claude Bernard Lyon 1
3 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

In this work, we recall the concept of contractive dynamics and its natural extension to the notion of differential dissipativity/passivity via the use of the so-called prolonged (or extended) system dynamics, obtained by lifting the system to the tangent bundle of the underlying manifold. The new concept of dissipative differential Hamiltonian dynamics is proposed providing a weaker notion of contractive dynamical system. Furthermore, the differential Hamiltonian notion is extended to the definition of differentially passive port-Hamiltonian system and we describe explicit conditions to exploit the 'natural' differential Hamiltonian function as differential storage function for the port-Hamiltonian system dynamics.

Keywords: Contractive systems differential passivity port-Hamiltonian systems dissipative Hamiltonian systems dissipative differential Hamiltonian system; Contractive systems; differential passivity; port-Hamiltonian systems; dissipative Hamiltonian systems; dissipative differential Hamiltonian system

Domains: Dynamical Systems [math.DS]

Mario Spirito, Bernhard Maschke, Yann Le Gorrec. Contraction Theory and Differential Passivity in the port-Hamiltonian formalism. 2024. ⟨hal-04479539v1⟩