Contraction Theory and Differential Passivity in the port-Hamiltonian formalism

Abstract

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. We describe explicit conditions to exploit the ‘natural’ Differential Hamiltonian function as differential storage function for the port-Hamiltonian system dynamics.