Coupling between hyperbolic and diffusive systems: A port-Hamiltonian formulation

Coupling between hyperbolic and diffusive systems: A port-Hamiltonian formulation

The aim of this paper is to study a conservative wave equation coupled to a diffusion equation. This coupled system naturally arises in musical acoustics when viscous and thermal effects at the wall of the duct of a wind instrument are taken into account. The resulting equation, known as Webster-Lokshin model, has variable coefficients in space, and a fractional derivative in time. This equatio...

Diffusive systems coupled to an oscillator: a Hamiltonian formulation

The aim of this paper is to study a conservative wave equation coupled to a diffusion equation : this coupled system naturally arises in musical acoustics when viscous and thermal effects at the wall of the duct of a wind instrument are taken into account. The resulting equation, known as Webster-Lokshin model, has variable coefficients in space, and a fractional derivative in time. The port-Ha...

On an intrinsic formulation of time-variant Port Hamiltonian systems

In this contribution we present an intrinsic description of time-variant Port Hamiltonian systems as they appear in modeling and control theory. This formulation is based on the splitting of the state bundle and the use of appropriate covariant derivatives, which guarantees that the structure of the equations is invariant with respect to time-variant coordinate transformations. In particular, w...

Discrete port-Hamiltonian systems

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling at the discrete level itself. One of the goals of this paper is to model port-Hamiltonian systems...

Distributed-Parameter Port-Hamiltonian Systems