ABSTRACT
This chapter discusses model reduction techniques of second-order index 3 descriptor systems. It can be shown that an index 3 system can be converted into an equivalent form of index 0 system by projecting it onto the hidden manifold. When model reduction is applied to the projected system, explicit formulation of the projected system is not required. We discuss both second-order-to-first-order and second-order-to-second-order reduction techniques. The low-rank alternating direction implicit (LR-ADI) iteration is also discussed for solving the projected Lyapunov equations of the underlying descriptor system efficiently in an implicit way. The theoretical results are illustrated by numerical experiments.
