ABSTRACT
This chapter discusses efficient techniques for the model reduction of large-scale first-order index 1 descriptor systems. Balanced truncation and interpolatory projection via the iterative rational Krylov algorithm (IRKA) are applied for the model reduction of such descriptor systems. We can show that by implementing some algebraic manipulation, the index 1 system can be converted into a generalized state space (GSS) system. However, in this conversion the original system loses the sparsity and becomes dense. In this chapter we show that model reduction can be performed without converting the index 1 system into the GSS system explicitly. To implement the balanced truncation we need to solve two continuous-time algebraic Lyapunov equations to compute the low-rank Gramian factors. We also discuss how to solve those Lyapunov equations efficiently and in an implicit way via low-rank ADI iteration. The efficiency of the proposed methods are shown through numerical experiments.
