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Analytic perturbation of Sylvester and Lyapunov matrix Konstantin E. Avrachenkov 1 Jean B. Lasserre 2
 

Summary: Analytic perturbation of Sylvester and Lyapunov matrix
equations
Konstantin E. Avrachenkov 1 Jean B. Lasserre 2
Abstract
We consider an analytic perturbation of the Sylvester
matrix equation. Mainly we are interested in the sin­
gular case, that is, when the null space of the unper­
turbed Sylvester operator is not trivial, but the per­
turbed equation has a unique solution. In this case, the
solution of the perturbed equation can be given in terms
of a Laurent series. Here we provide a necessary and
suOEcient condition for the existence of a Laurent series
with a ørst order pole. An eOEcient recursive procedure
for the calculation of the Laurent series' coeOEcients is
given. Finally, we show that in the particular, but prac­
tically important case of semisimple eigenvalues, the re­
cursive procedure can be written in a compact matrix
form.
1 Introduction
The Sylvester matrix equation AX+XB = C (or Lya­

  

Source: Avrachenkov, Konstantin - INRIA Sophia Antipolis

 

Collections: Computer Technologies and Information Sciences