Asymptotic Stability and Strict Passivity of Port-Hamiltonian Descriptor Systems via State Feedback

TL;DR

This paper establishes conditions under which port-Hamiltonian descriptor systems can be made asymptotically stable and strictly passive through state feedback, while maintaining their structure.

Contribution

It provides necessary and sufficient conditions for achieving asymptotic stability, strict passivity, regularity, and index one property via state feedback in port-Hamiltonian descriptor systems.

Findings

Conditions for asymptotic stability via state feedback

Criteria for strict passivity preservation

Preservation of port-Hamiltonian structure

Abstract

While port-Hamiltonian descriptor systems are known to be stable and passive, they may not be asymptotically stable or strictly passive. Necessary and sufficient conditions are presented when these properties as well as the regularity and the index one property can be achieved via state feedback while preserving the port-Hamiltonian structure.