ABSTRACT
This chapter discusses the balanced truncation and interpolatory projection methods for the model reduction of first-order index 3 descriptor systems. By projecting the system onto the hidden manifold where the solution of the descriptor system exists, we can convert the system into a generalized state space model. However, the converted system becomes dense even if the original one is sparse. This chapter will show that the model reduction methods can be carried out without explicitly forming the generalized system. Moreover we discuss how to solve the projected Lyapunov equations by handling the descriptor implicitly to compute the low-rank Gramian factors which are used to perform the balancing based model reduction. The effectiveness of the proposed techniques are illustrated by numerical experiments.
