Coefficient-level output-feedback stabilization of linear port-Hamiltonian descriptor systems

TL;DR

This paper develops coefficient-level conditions for stabilizing linear port-Hamiltonian descriptor systems using output feedback, avoiding explicit pH representations and enabling flexible gain choices.

Contribution

It introduces a novel coefficient-level framework for output-feedback stabilization that preserves port-Hamiltonian structure without explicit pH form computation.

Findings

Derived conditions ensure closed-loop stability and port-Hamiltonian properties.

Extended framework to proportional-derivative output feedback with order assignment.

Allows arbitrary symmetric positive definite proportional gain without explicit pH representation.

Abstract

This paper studies coefficient-level, structure-preserving output-feedback stabilization of linear port-Hamiltonian (pH) descriptor systems. Existing stabilization conditions generally require explicit pH representations, which may be costly to compute. We consider descriptor systems for which only the coefficient matrices are available and for which a pH representation is known to exist but is not explicitly given. For proportional output feedback, we derive coefficient-level conditions that are equivalent to the known solvability criteria in the explicit pH setting. These conditions ensure that the closed-loop system is regular, impulse-free, asymptotically stable, and remains port-Hamiltonian. We further extend the framework to proportional-derivative output feedback and enable the assignment of a prescribed dynamical order. Under the proposed conditions, the proportional gain may be chosen as any symmetric positive definite matrix, and the derivative gain is constructed from coefficient-based decompositions, without computing a pH representation.