SOPRBT - Passivity-Preserving Model Reduction for Second Order Systems

This MATLAB code implements a model reduction algorithm for second order systems based on positive real-balanced truncation. This algorithm preserves stability, passivity, and restores the second order structure of the system by indefinite linear algebra techniques.

The method requires the solution of a large-scale Lur'e equation. We make use of the method [2] in conjunction the RADI algorithm [3] with LDL^T-factored iterates for solving the projected algebraic Riccati equations constructed in [2]. This code has been tested using an unpublished version of M-M.E.S.S. [4], GIT repository tag bc7be0cd5154201b3f988ef3a52f119406e173e7 and should work with any version *later* than 2.0.1.

The main file of this package is soprbt.m, while the numerical results from the revised version of [1] can be created by calling test_soprbt.m.

EXTERNAL CODES INCLUDED:

   - sparsenull, see [5].

REFERENCES:

[1] I. Dorschky, T. Reis and M. Voigt. Balanced truncation model reduction for symmetric second-order systems - a passivity based approach, Preprint arXiv:2006.09170, 2020.
[2] F. Poloni, R. Reis. A deflation approach for large-scale Lur'e equations. SIAM J. Matrix Anal. Appl., 33(4):1339-1368, 2012.
[3] P. Benner, Z. Bujanović, P. Kürschner, and J. Saak. RADI: A low-rank ADI-type algorithm for large scale algebraic Riccati equations, Numer. Math., 138(2), 301-330, 2018.
[4] J. Saak, M. Koehler, P. Benner. Matrix equations, sparse solvers: M-M.E.S.S.-2.0.1 - philosophy, features and application for (parametric) model order reduction, Preprint arXiv:2003.02088, March 2020.
[5] P. Kowal. Null space of a sparse matrix (https://www.mathworks.com/matlabcentral/fileexchange/11120-null-space-of-a-sparse-matrix), MATLAB Central File Exchange. 2021.