An Iterative Model Order Reduction Scheme for a Special Class of Bilinear Descriptor Systems Appearing in Constraint Circuit Simulation

We focus on interpolatory-based model order reduction for a special class of bilinear descriptor systems in the H2-optimal framework, appearing in constraint circuit simulations. The straightforward extension of the H2-optimality conditions for ODE systems to descriptor systems generically may produce an unbounded error in the H2 or H∞ norm, or both. This arises due to the inappropriate use of the polynomial part of the system. To ensure bounded error, one needs to deal with the polynomial part of the systems properly. To do so, we first transform these descriptor systems into equivalent ODE systems by means of oblique projectors, as it is widely done in the literature for linear index-2 ODEs. This enables us to employ bilinear iterative rational Krylov algorithm (B-IRKA) which provides us locally H2-optimal reducedorder systems on convergence, if it converges. Unfortunately, the direct implementation of BIRKA on equivalent ODEs requires the expensive explicit computation of the oblique projectors. Therefore, as one of our contributions, we show how to apply B-IRKA to the equivalent bilinear ODE system without an explicit computation of the projectors. We demonstrate the efficiency of the proposed technique by means of several constraint circuit examples and compare the quality of the reduced-order systems with the ones obtained by using the projection matrices determined by applying IRKA on the corresponding linear part.