Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

A note on recursive schur complements, block hurwitz stability of metzler matrices, and related results

It is known that the stability of a Metzler matrix can be characterized in a Routh-Hurwitz-like fashion based on a recursive application of scalar Schur complements [1]. Our objective in this brief note is to show that recently obtained stability conditions are equivalent statements of this result and can be deduced directly there from using only elementary results from linear algebra. Implications of this equivalence are also discussed and several examples are given to illustrate potentially interesting system-theoretic applications of this observation62841674172This work was supported in part by the Science Foundation Ireland under grant 11/PI/117