Well-posedness and Stability of Linear Port-Hamiltonian Systems with Nonlinear Boundary Feedback

TL;DR

This paper extends stability results for linear port-Hamiltonian systems to include nonlinear boundary feedback, introducing a design method for nonlinear controllers and demonstrating its application on the Euler-Bernoulli beam.

Contribution

It develops a novel approach for nonlinear boundary feedback stabilization of port-Hamiltonian systems, expanding existing linear results to nonlinear control.

Findings

Stability results are extended to nonlinear dissipative boundary feedback.

A new design method for nonlinear controllers is proposed.

Application demonstrated on the Euler-Bernoulli beam.

Abstract

Boundary feedback stabilisation of linear port-Hamiltonian systems on an interval is considered. Generation and stability results already known for linear feedback are extended to nonlinear dissipative feedback, both to static feedback control and dynamic control via an (exponentially stabilising) nonlinear controller. A design method for nonlinear controllers of linear port-Hamiltonian systems is introduced. As a special case the Euler-Bernoulli beam is considered.