Summary: A modified low­rank Smith method for large­scale Lyapunov equations 
S. GUGERCIN y , D.C. SORENSEN z , and A.C. ANTOULAS y
e­mail: fserkan,sorensen,acag@rice.edu
August 13, 2002
Abstract
In this note we present a modified cyclic low­rank Smith method to compute low­rank approximations to
solutions of Lyapunov equations arising from large­scale dynamical systems. Unlike the original cyclic low­
rank Smith method introduced by Penzl in [19], the number of columns required by the modified method in the
approximate solution does not necessarily increase at each step and is usually much lower than in the original
cyclic low­rank Smith method. The modified method never requires more columns than the original one. Upper
bounds are established for the errors of the low­rank approximate solutions and also for the errors in the resulting
approximate Hankel singular values. Numerical results are given to verify the efficiency and accuracy of the
new algorithm.
1 Introduction
Linear time invariant (LTI) systems
 :

_
x(t) = Ax(t) +Bu(t)
y(t) = Cx(t) +Du(t)

Source: Antoulas, Athanasios C. - Department of Electrical and Computer Engineering, Rice University

Collections: Engineering