Structure-preserving model reduction of second-order systems by Krylov subspace methods

Laguerre-Gramian-based structure-preserving model order reduction for second-order form systems

“…Note that preservation of the second-order structure in the ROM allows a meaningful physical interpretation and usually provides more accurate approximations, and an ROM which preserves the structural properties such as stability and passivity is highly desirable. Therefore, on the contrary, structure-preserving MOR techniques for second-order form systems are proposed, which have received a lot of attention during the last few years, including moment matching methods based on Krylov subspaces (Bai and Su, 2005;Jbilou and Kaouane, 2019;Xu et al, 2018), families of BT methods (Chahlaoui et al, 2006;Haider et al, 2019;Reis and Stykel, 2008;Uddin, 2020) and orthogonal polynomial methods (Qiu et al, 2018;Xiao et al, 2019b;Xiao and Jiang, 2014). Overview articles of different reduction methods are given in Antoulas (2005), Benner et al (2017), Jiang (2010) and the references therein.…”

Structure preserving balanced proper orthogonal decomposition for second‐order form systems via shifted Legendre polynomials

“…For engineering control and design of such a system, it is highly desirable to obtain a ROM which preserves the physically interpretable structure and the essential properties of the original model, such as stability and passivity. On the contrary, the others are structure preserving MOR techniques for second‐order form systems, which have received a lot of attention during the last few years including the families of balanced truncation (BT) [9, 10] methods, moment matching methods based on Krylov subspace [11, 12] and orthogonal polynomials methods [13, 14]. Overview articles of different reduction methods are given in [3, 15] and the references therein.…”