  Linear quadratic Gaussian (LQG) control design for port-Hamiltonian systems
is studied. The recently proposed method from [42] is reviewed and modified
such that the resulting controllers have a port-Hamiltonian (pH) realization.
Based on this new modification, a reduced-order controller is obtained by
truncation of a balanced system. The approach is shown to be closely related to
classical LQG balanced truncation and shares a similar a priori error bound
with respect to the gap metric. With regard to this error bound, a
theoretically optimal pH-representation is derived. Consequences for
pH-preserving balanced truncation model reduction are discussed and shown to
yield two different classical H-infinity-error bounds. Numerical examples
illustrate the main theoretical findings.
