Model reduction by second order Krylov subspaces: Extensions, stability and proportional damping

A discussion on second order Krylov subspace methods for the reduction of second order systems by applying a direct projection to the original model is presented with the following new results: (i) matching the moments about different expansion points, simultaneously, (ii) matching the Markov parameters, (iii) conditions to preserve stability of the original system, (iv) reducing second order systems with proportional damping, where the projection matrix can be derived independently of the damping matrix, (v) generalizing the method to reduce models with higher order structures