Exponential stability for infinite-dimensional non-autonomous port-Hamiltonian Systems

TL;DR

This paper establishes the exponential stability of non-autonomous infinite-dimensional port-Hamiltonian systems, demonstrating well-posedness and energy decay under dissipation conditions using evolution family theory.

Contribution

It extends exponential stability results from autonomous to non-autonomous port-Hamiltonian systems, providing well-posedness and energy decay analysis.

Findings

Proves $C^1$-well-posedness for the non-autonomous system.

Shows energy decays exponentially under dissipation conditions.

Extends autonomous stability results to non-autonomous systems.

Abstract

We study the non-autonomous version of an infinite-dimensional port-Hamiltonian system on an interval $[a, b]$. Employing abstract results on evolution families, we show $C^1$-well-posedness of the corresponding Cauchy problem, and thereby existence and uniqueness of classical solutions for sufficiently regular initial data. Further, we demonstrate that a dissipation condition in the style of the dissipation condition sufficient for uniform exponential stability in the autonomous case also leads to a uniform exponential decay of the energy in this non-autonomous setting.