Model reduction of second order systems

In this chapter, the problem of constructing a reduced order system while preserving the second order structure of the original system is discussed. After a brief introduction on second order systems and a review of first order model reduction techniques, two classes of second order structure preserving model reduction techniques Krylov subspace-based and SVD-based are presented. For the Krylov techniques, conditions on the projectors that guarantee the reduced second order system tangentially interpolates the original system at given frequencies are derived and an algorithm is described. For SVD-based techniques, a Second Order Balanced Truncation method is derived from second order gramians