文献类型：期刊文献

英文题名：Krylov subspace type methods for solving projected generalized continuous-time Lyapunov equations

作者：Zhou, Yujian[1]; Lin, Yiqin[1]; Bao, Liang[2]

机构：[1] Hunan University of Science and Engineering, Institute of Computational Mathematics, Yangzhitang Road 130, 425100 Yongzhou, China; [2] East China University of Science and Technology, Department of Mathematics, Meilong Road 130, 200237 Shanghai, China

年份：2012

卷号：11

期号：12

起止页码：1114

外文期刊名：WSEAS Transactions on Mathematics

收录：EI(收录号：20130415931329)

语种：英文

外文关键词：Lyapunov functions - Continuous time systems

摘要：In this paper we consider the numerical solution of projected generalized continuous-time Lyapunov equations with low-rank right-hand sides. The interest in this problem stems from stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. Two projection methods are proposed for calculating low-rank approximate solutions. One is based on the usual Krylov subspace, while the other is based on the union of two different Krylov subspaces. The former is the Krylov subspace method and the latter is the extended Krylov subspace method. For these two methods, exact expressions for the norms of residuals are derived and results on finite termination are presented. Numerical experiments in this paper show the effectiveness of the proposed methods.