A Parameter Free Iterative Method for Solving Projected Generalized Lyapunov Equations

Abstract

This paper is devoted to the numerical solution of projected generalized continuous-time Lyapunov equations with low-rank right-hand sides.Such equations arise in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation.A parameter free iterative method is proposed.This method is based upon a combination of an approximate power method and a generalized ADI method.Numerical experiments presented in this paper show the effectiveness of the proposed method.