L2-optimal model reduction for unstable systems using iterative rational Krylov algorithm

Unstable dynamical systems can be viewed from a variety of perspectives. We discuss the potential of an inputoutput map associated with an unstable system to represent a bounded map from L2(R) to itself and then develop criteria for optimal reduced order approximations to the original (unstable) system with respect to an L2-induced Hilbert-Schmidt norm. Our optimality criteria extend the Meier-Luenberger interpolation conditions for optimal H2 approximation of stable dynamical systems. Based on this interpolation framework, we describe an iteratively corrected rational Krylov algorithm for L2 model reduction. A numerical example involving a hardto-approximate full-order model illustrates the effectiveness of the proposed approach.