Error bounds for port-Hamiltonian model and controller reduction based on system balancing

We study linear quadratic Gaussian (LQG) control design for port-Hamiltonian systems. To this end, we exploit the freedom in choosing weighting matrices and propose a specific choice which leads to an LQG controller is and, thus, particular stable passive. Furthermore, construct reduced-order via balancing subsequent truncation. This approach closely related classical balanced truncation shares similar priori error bound with respect gap metric. By exploiting non-uniqueness of Hamiltonian, are able determine optimal pH representation full-order system sense that minimized. In addition, discuss consequences pH-preserving model reduction results two different H?-error bounds. Finally, illustrate theoretical findings by means numerical examples.