Model reduction of quadratic-bilinear descriptor systems via Carleman bilinearization

We propose a model reduction technique for quadratic-bilinear descriptor systems. The approach involves approximating the system by a bilinear descriptor system using Carleman bilinearization [1]. It is shown that, by assuming a particular structure of the matrix pencil, the bilinearization process preserves the structure of the matrix pencil in the bilinearized system. Further, we extend the use of the bilinear iterative rational Krylov algorithm (B-IRKA) [2] to descriptor systems to identify a locally ℋ₂-optimal reduced-order system for the bilinearized system under the assumption that the ℋ₂ norm of the system exists. Applications to the simulation of a nonlinear RC circuit and a lid-driven cavity flow are presented to illustrate the proposed methodology.