Rational Krylov subspace method (RKSM) for solving the Lyapunov equations of index-1 descriptor systems and application to balancing based model reduction

This paper focuses on the iterative method for solving Lyapunov equations to compute the low-rank Gramian factors. Such Lyapunov equations arise from large-scale sparse index-1 descriptor system. The technique is mainly based on rational Krylov subspace method (RKSM) which is introduced in [1]. However, there the proposed technique is applicable for the standard state space model. Here, we extend this idea for index-1 descriptor system to compute the low-rank Gramian factors. The Gramian factors are then applied to the balancing based model reduction to reduce the complexity of the underlying system. Several test examples are considered to show the efficiency of the proposed method numerically.