Structure-preserving approximation of distributed-parameter second-order systems using Krylov subspaces

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In this article, the approximation of linear second-order distributed-parameter systems (DPS) is considered using a Galerkin approach. The resulting finite-dimensional approximation model also has a second-order structure and preserves the stability as well as the passivity. Furthermore, by extending the Krylov subspace methods for finite-dimensional systems of second order to DPS, the basis vectors of the Galerkin projection are determined such that the transfer behaviour of the DPS can be approximated by using moment matching. The structure-preserving approximation of an Euler–Bernoulli beam with Kelvin–Voigt damping demonstrates the results of the article.