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Numerical solution of large Lyapunov equationsA few methods are proposed for solving large Lyapunov equations that arise in control problems. The common case where the right hand side is a small rank matrix is considered. For the single input case, i.e., when the equation considered is of the form AX + XA(sup T) + bb(sup T) = 0, where b is a column vector, the existence of approximate solutions of the form X = VGV(sup T) where V is N x m and G is m x m, with m small is established. The first class of methods proposed is based on the use of numerical quadrature formulas, such as Gauss-Laguerre formulas, applied to the controllability Grammian. The second is based on a projection process of Galerkin type. Numerical experiments are presented to test the effectiveness of these methods for large problems.
Document ID
19900014694
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Saad, Youcef (Research Inst. for Advanced Computer Science Moffett Field, CA, United States)
Date Acquired
September 6, 2013
Publication Date
May 1, 1989
Subject Category
Numerical Analysis
Report/Patent Number
NAS 1.26:180359
RIACS-TR-89.20
NASA-CR-180359
Accession Number
90N24010
Funding Number(s)
CONTRACT_GRANT: NCC2-387
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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