Patil, Deepak; Tesi, Pietro; Trenn, Stephan Indiscernible topological variations in DAE networks Unpublished 2017. @unpublished{PatiTesi17pp, title = {Indiscernible topological variations in DAE networks}, author = {Deepak Patil and Pietro Tesi and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/11/Preprint-PTT171123.pdf, Preprint}, year = {2017}, date = {2017-11-23}, abstract = {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 conditions simplifies to 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a topological change preserves regularity of the nominal network.}, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } A problem of characterizing conditions under which a topological change in a network of differential algebraic equations (DAEs) can go undetected is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 conditions simplifies to 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. |

Tanwani, Aneel; Trenn, Stephan Detectability and Observer Design for Switched Differential Algebraic Equations Unpublished 2017. @unpublished{TanwTren17pp, title = {Detectability and Observer Design for Switched Differential Algebraic Equations}, author = {Aneel Tanwani and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/11/Preprint-TT171116.pdf, Preprint}, year = {2017}, date = {2017-11-16}, abstract = {This paper studies detectability for switched linear differential-algebraic equations (DAEs) and its application to the synthesis of observers, which generate asymptotically converging state estimates. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor at the end of that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component of the system is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption. }, keywords = {}, pubstate = {published}, tppubtype = {unpublished} } This paper studies detectability for switched linear differential-algebraic equations (DAEs) and its application to the synthesis of observers, which generate asymptotically converging state estimates. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor at the end of that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component of the system is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption. |

# Submitted

Indiscernible topological variations in DAE networks Unpublished 2017. |

Detectability and Observer Design for Switched Differential Algebraic Equations Unpublished 2017. |