Implicit Volterra series interpolation for model reduction of bilinear systems

Linear systems where the affine parameter dependence is given as low-rank variation in the state matrix can be mapped into a non-parameterized multi-input multi-output linear system. This allows us to utilize the standard (non-parametric) linear IRKA (Gugercin et al., 2008) for the problem of parameterized/bilinear interpolation. Numerical results show that the approximations are of comparable accuracy to those obtained from the bilinear iterative rational Krylov algorithm (Benner and Breiten, 2012). The proposed approach, however, has the advantage that it reduces the computational costs as it involves computations associated with solving linear systems only.