Interpolatory projection methods for structure-preserving model reduction

We present a framework for interpolatory model reduction that treats systems having a generalized coprime factorization C(s)(s)−1B(s)+DC(s)(s)−1B(s)+D. This includes rational Krylov-based interpolation methods as a special case. The broader framework allows retention of special structure in reduced models such as symmetry, second- and higher order structure, state constraints, internal delays, and infinite dimensional subsystems. Two numerical examples are provided for systems associated with viscoelastic dynamics and with an internal state delay that demonstrate the effectiveness and flexibility of the approach.