Stabilization of linear Port-Hamiltonian Descriptor Systems via Output Feedback

TL;DR

This paper provides a complete solution for stabilizing linear port-Hamiltonian descriptor systems using output feedback, ensuring asymptotic stability while preserving the system's structure.

Contribution

It offers necessary and sufficient conditions for the existence of output feedback that stabilizes port-Hamiltonian descriptor systems, a problem previously only partially understood.

Findings

Complete characterization of stabilizing output feedbacks for pHDAE systems.

Conditions ensuring regularity and index at most one after feedback.

Theoretical framework for structure-preserving stabilization.

Abstract

The structure preserving stabilization of (possibly non-regular) linear port-Hamiltonian descriptor (pHDAE) systems by output feedback is discussed. For general descriptor systems the characterization when there exist output feedbacks that lead to an asymptotically stable closed loop system is a very hard and partially an open problem. In contrast to this it is shown that for systems in pHDAE representation this problem can be completely solved. Necessary and sufficient conditions are presented that guarantee that there exist a proportional and/or derivative output feedback such that the resulting closed-loop port-Hamiltonian descriptor system is asymptotically stable. For this it is also necessary that the output feedback also makes the problem regular and of index at most one. A complete characterization when this is possible is presented as well.