Idempotent relations, semi-projections, and generalized inverses. - In: Contributions to mathematics and statistics, (2021), S. 87-110
Balanced truncation model reduction for symmetric second order systems - a passivity-based approach. - In: SIAM journal on matrix analysis and applications, ISSN 1095-7162, Bd. 42 (2021), 4, S. 1602-1635
We introduce a model reduction approach for linear time-invariant second order systems based on positive real balanced truncation. Our method guarantees to preserve asymptotic stability and passivity of the reduced order model as well as the positive definiteness of the mass and stiffness matrices. Moreover, we receive an a priori gap metric error bound. Finally we show that our method based on positive real balanced truncation preserves the structure of overdamped second order systems.
https://doi.org/10.1137/20M1346109
Some notes on port-Hamiltonian systems on Banach spaces. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 19, S. 223-229
We consider port-Hamiltonian systems from a functional analytic perspective. Dirac structures and Hamiltonians on Banach spaces are introduced, and an energy balance is proven. Further, we consider port-Hamiltonian systems on Banach manifolds, and we present some physical examples that fit into the presented theory.
https://doi.org/10.1016/j.ifacol.2021.11.082