WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
Krylov Subspace Type Methods for Solving Projected Generalized Continuous-Time Lyapunov Equations
Authors: , ,
Abstract: 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.
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Keywords: Projected generalized Lyapunov equation, Projection method, Krylov subspace, Alternating direction implicit method, Matrix pencil, C-stable