We have submitted the manuscript
Patil, Deepak; Tesi, Pietro; Trenn, Stephan
Indiscernible topological variations in DAE networks Journal Article
In: Automatica, vol. 101, pp. 280-289, 2019.
A problem of characterizing conditions under which a topological change in a network of differential algebraic equations (DAEs) can go undetected is considered. It is shown that initial conditions for which topological changes are indiscernible belong to a generalized eigenspace shared by the nominal system and the system resulting from a topological change. A condition in terms of eigenvectors of the nominal system is derived to check for existence of possibly indiscernible topological changes. For homogenous networks this condition simplifies to the existence of an eigenvector of the Laplacian of network having equal components. Lastly, a rank condition is derived which can be used to check if a topological change preserves regularity of the nominal network.
for publication. It is an extension of our IFAC paper
Küsters, Ferdinand; Patil, Deepak; Tesi, Pietro; Trenn, Stephan
In: Proc. 20th IFAC World Congress 2017, pp. 7333 - 7338, Toulouse, France, 2017, ISSN: 2405-8963.
The ability to detect topology variations in dynamical networks defined by differential algebraic equations (DAEs) is considered. We characterize the existence of initial states, for which topological changes are indiscernible. A key feature of our characterization is the ability to verify indiscernibility just in terms of the nominal topology. We apply the results to a power grid model and also discuss the relationship to recent mode-detection results for switched DAEs.
where we extended the results to the MIMO case and also fully characterize the set of indiscernible initial states. Furthermore, we present sufficient conditions for regularity preserving topological changes.