Structure Preserving $H_\infty$ Control for Port-Hamiltonian Systems

TL;DR

This paper develops a method for designing $H_ fty$ controllers for port-Hamiltonian systems that preserves their structure, and demonstrates that balanced truncation can maintain this structure in reduced models.

Contribution

It introduces a modified Riccati equation approach ensuring port-Hamiltonian structure in $H_ abla$ control design and model reduction.

Findings

Modified Riccati equations preserve port-Hamiltonian structure.

Balanced truncation maintains structure in reduced models.

System representation influences approximation quality.

Abstract

We study $H_\infty$ control design for linear time-invariant port-Hamiltonian systems. By a modification of the two central algebraic Riccati equations, we ensure that the resulting controller will be port-Hamiltonian. Using these modified equations, we proceed to show that a corresponding balanced truncation approach preserves port-Hamiltonian structure. We illustrate the theoretical findings using numerical examples and observe that the chosen representation of the port-Hamiltonian system can have an influence on the approximation qualities of the reduced order model.