Model Reduction of Linear Port-Hamiltonian Systems: A Structure Preserving Approach

In this note we address the problem of model reduction of a particular class of linear systems, namely, the linear port-Hamiltonian (PH) systems. Furthermore, we explore the preservation of the PH structure in the reduced model. Towards this end, we adopt the balanced truncation approach to reduced the order of the model, in particular, we study the use of extended Gramians to balance the linear PH systems. The latter provides degrees of freedom to impose a desired structure, in this case a PH one, to the reduced model. Moreover, for balanced truncation using extended Gramians, the error bound is well-known and is given in terms of the Hankel singular values of the truncated state